Calabi-Yau differential operator database v.3.0

1

New Number: 2.10 | AESZ: 70 | Superseeker: 27 18089 | Hash: 3d2adae6eaf26a56c76b8b67d92cc5df

Degree: 2

$\theta^4-3 x(3\theta+1)(3\theta+2)(10\theta^2+10\theta+3)+3^{4} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Coefficients of the holomorphic solution: 1, 18, 1350, 156240, 22141350, ...
--> OEIS
Normalized instanton numbers (n₀=1): 27, 432, 18089, 997785, 68438142, ... ; Common denominator:...

Discriminant

$(243z-1)(27z-1)$

Local exponents

$0$ $\frac{ 1}{ 243}$ $\frac{ 1}{ 27}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 3}$
$0$ $1$ $1$ $\frac{ 2}{ 3}$
$0$ $1$ $1$ $\frac{ 4}{ 3}$
$0$ $2$ $2$ $\frac{ 5}{ 3}$

\(0\)	\(\frac{ 1}{ 243}\)	\(\frac{ 1}{ 27}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 3}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 2}{ 3}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 4}{ 3}\)
\(0\)	\(2\)	\(2\)	\(\frac{ 5}{ 3}\)

Note:

Hadamard product $B\ast c$.

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-156\)	\(72\)	\(18\)	\(9\)

2

New Number: 2.11 | AESZ: 69 | Superseeker: 64 246848 | Hash: 729adc350de26d9415643078ed8d3867

Degree: 2

$\theta^4-2^{2} x(4\theta+1)(4\theta+3)(10\theta^2+10\theta+3)+2^{4} 3^{2} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 36, 6300, 1718640, 575675100, ...
--> OEIS
Normalized instanton numbers (n₀=1): 64, 2616, 246848, 32024824, 5160268864, ... ; Common denominator:...

Discriminant

$(576z-1)(64z-1)$

Local exponents

$0$ $\frac{ 1}{ 576}$ $\frac{ 1}{ 64}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 4}$
$0$ $1$ $1$ $\frac{ 3}{ 4}$
$0$ $1$ $1$ $\frac{ 5}{ 4}$
$0$ $2$ $2$ $\frac{ 7}{ 4}$

\(0\)	\(\frac{ 1}{ 576}\)	\(\frac{ 1}{ 64}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 4}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 3}{ 4}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 5}{ 4}\)
\(0\)	\(2\)	\(2\)	\(\frac{ 7}{ 4}\)

Note:

Hadamard product $C\ast c$

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-224\)	\(72\)	\(12\)	\(8\)

3

New Number: 2.12 | AESZ: 64 | Superseeker: 432 78259376 | Hash: 43991f21e20c16ab91690259b788b4cd

Degree: 2

$\theta^4-2^{2} 3 x(6\theta+1)(6\theta+5)(10\theta^2+10\theta+3)+2^{4} 3^{4} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 180, 207900, 379819440, 855338063580, ...
--> OEIS
Normalized instanton numbers (n₀=1): 432, 130842, 78259376, 68104755558, 73096116588720, ... ; Common denominator:...

Discriminant

$(3888z-1)(432z-1)$

Local exponents

$0$ $\frac{ 1}{ 3888}$ $\frac{ 1}{ 432}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 6}$
$0$ $1$ $1$ $\frac{ 5}{ 6}$
$0$ $1$ $1$ $\frac{ 7}{ 6}$
$0$ $2$ $2$ $\frac{ 11}{ 6}$

\(0\)	\(\frac{ 1}{ 3888}\)	\(\frac{ 1}{ 432}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 6}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 5}{ 6}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 7}{ 6}\)
\(0\)	\(2\)	\(2\)	\(\frac{ 11}{ 6}\)

Note:

Hadamard product $B\ast c$.

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-364\)	\(72\)	\(6\)	\(7\)

4

New Number: 2.13 | AESZ: 36 | Superseeker: 16 1232 | Hash: dea6fdf568a5907a24ba30fef2caf124

Degree: 2

$\theta^4-2^{4} x(2\theta+1)^2(3\theta^2+3\theta+1)+2^{9} x^{2}(2\theta+1)^2(2\theta+3)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 16, 720, 44800, 3312400, ...
--> OEIS
Normalized instanton numbers (n₀=1): 16, 42, 1232, 32159, 990128, ... ; Common denominator:...

Discriminant

$(128z-1)(64z-1)$

Local exponents

$0$ $\frac{ 1}{ 128}$ $\frac{ 1}{ 64}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $\frac{ 3}{ 2}$
$0$ $2$ $2$ $\frac{ 3}{ 2}$

\(0\)	\(\frac{ 1}{ 128}\)	\(\frac{ 1}{ 64}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 3}{ 2}\)
\(0\)	\(2\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

A*d

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-88\)	\(80\)	\(32\)	\(12\)

5

New Number: 2.14 | AESZ: 48 | Superseeker: 24 5832 | Hash: 8081a3989d09a7d612953dac3341d90c

Degree: 2

$\theta^4-2^{2} 3 x(3\theta+1)(3\theta+2)(3\theta^2+3\theta+1)+2^{5} 3^{2} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 24, 1800, 188160, 23423400, ...
--> OEIS
Normalized instanton numbers (n₀=1): 24, 291/2, 5832, 247116, 12634944, ... ; Common denominator:...

Discriminant

$(216z-1)(108z-1)$

Local exponents

$0$ $\frac{ 1}{ 216}$ $\frac{ 1}{ 108}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 3}$
$0$ $1$ $1$ $\frac{ 2}{ 3}$
$0$ $1$ $1$ $\frac{ 4}{ 3}$
$0$ $2$ $2$ $\frac{ 5}{ 3}$

\(0\)	\(\frac{ 1}{ 216}\)	\(\frac{ 1}{ 108}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 3}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 2}{ 3}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 4}{ 3}\)
\(0\)	\(2\)	\(2\)	\(\frac{ 5}{ 3}\)

Note:

B*d

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-162\)	\(84\)	\(24\)	\(11\)

6

New Number: 2.15 | AESZ: 38 | Superseeker: 48 73328 | Hash: 9ce26bb7405c3b98d8aeae5b1102c611

Degree: 2

$\theta^4-2^{4} x(4\theta+1)(4\theta+3)(3\theta^2+3\theta+1)+2^{9} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 48, 8400, 2069760, 609008400, ...
--> OEIS
Normalized instanton numbers (n₀=1): 48, 998, 73328, 7388135, 857248528, ... ; Common denominator:...

Discriminant

$(512z-1)(256z-1)$

Local exponents

$0$ $\frac{ 1}{ 512}$ $\frac{ 1}{ 256}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 4}$
$0$ $1$ $1$ $\frac{ 3}{ 4}$
$0$ $1$ $1$ $\frac{ 5}{ 4}$
$0$ $2$ $2$ $\frac{ 7}{ 4}$

\(0\)	\(\frac{ 1}{ 512}\)	\(\frac{ 1}{ 256}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 4}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 3}{ 4}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 5}{ 4}\)
\(0\)	\(2\)	\(2\)	\(\frac{ 7}{ 4}\)

Note:

Hadamard product $C\ast d$

Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 48, 8032, 1979904, 472848672, 107156066048, 24205631604736, 5536680545574912,...
Coefficients of the q-coordinate : 0, 1, -208, 32000, -4613120, 605381040, -78889707008, 9643425928192,...

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

Explicit solution

$A_{n}=\dbinom{2n}{n}\dbinom{4n}{2n}\sum_{k=0}^{n}\dbinom{n}{k}\dbinom{2k}{k}\dbinom{2n-2k}{n-k}$

Maple LaTex

Characteristic classes:

$C_3$	$C_2 H$	$H^3$	$ \vert H \vert$
$-268$	$88$	$16$	$10$

Monodromy (with respect to Frobenius basis)

$1$	$-1$	$\frac{ 1}{ 2}$	$-\frac{ 1}{ 6}$
$0$	$1$	$-1$	$\frac{ 1}{ 2}$
$0$	$0$	$1$	$-1$
$0$	$0$	$0$	$1$

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$1+268\lambda$	$0$	$Iarctan(\frac{ 173}{ 564})$	$.105419378$
$\frac{ 11}{ 3}$	$1$	$\frac{ 121}{ 144}$	$-Iarctan(\frac{ 173}{ 564})$
$0$	$0$	$1$	$0$
$16$	$0$	$\frac{ 11}{ 3}$	$1-268\lambda$

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$\frac{ 19}{ 6}+4Iln(2)^{ \frac{ 6}{ 5}}Zeta(5)^(\frac{ 2}{ 9})$	$-\frac{ 13}{ 24}-134\lambda$	$.49652777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778+.595253091I$	$.64137367e-1-.351740463I$
$\frac{ 22}{ 3}+\frac{ 3}{ 1000000000}I$	$-\frac{ 5}{ 6}+\frac{ 1}{ 500000000}I$	$\frac{ 121}{ 72}-\frac{ 1}{ 500000000}I$	$-.49652777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778-.595253091I$
$8+\frac{ 3}{ 1000000000}I$	$-2+\frac{ 1}{ 500000000}I$	$\frac{ 17}{ 6}-\frac{ 1}{ 500000000}I$	$-\frac{ 13}{ 24}-134\lambda$
$32+\frac{ 7}{ 500000000}I$	$-8+\frac{ 7}{ 1000000000}I$	$\frac{ 22}{ 3}-\frac{ 7}{ 1000000000}I$	$-\frac{ 7}{ 6}-4Iln(2)^{ \frac{ 6}{ 5}}Zeta(5)^(\frac{ 2}{ 9})$

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Basis of the Doran-Morgan lattice

$-268\lambda$	$\frac{ 19}{ 3}$	$1$	$1$
$-\frac{ 11}{ 3}$	$-8$	$-1$	$0$
$0$	$16$	$0$	$0$
$-16$	$0$	$0$	$0$

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7

New Number: 2.16 | AESZ: 65 | Superseeker: 240 19105840 | Hash: 13ba368bcbb10731ac8727b510731ff2

Degree: 2

$\theta^4-2^{4} 3 x(6\theta+1)(6\theta+5)(3\theta^2+3\theta+1)+2^{9} 3^{2} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 240, 277200, 457416960, 904864680720, ...
--> OEIS
Normalized instanton numbers (n₀=1): 240, 57102, 19105840, 14810143935, 10017820614480, ... ; Common denominator:...

Discriminant

$(3456z-1)(1728z-1)$

Local exponents

$0$ $\frac{ 1}{ 3456}$ $\frac{ 1}{ 1728}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 6}$
$0$ $1$ $1$ $\frac{ 5}{ 6}$
$0$ $1$ $1$ $\frac{ 7}{ 6}$
$0$ $2$ $2$ $\frac{ 11}{ 6}$

\(0\)	\(\frac{ 1}{ 3456}\)	\(\frac{ 1}{ 1728}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 6}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 5}{ 6}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 7}{ 6}\)
\(0\)	\(2\)	\(2\)	\(\frac{ 11}{ 6}\)

Note:

Hadamard product D*d

Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 240, 457056, 515857920, 947849668896, 1252227576810240, 1951472479155996672, 2805919645433093677056,...
Coefficients of the q-coordinate : 0, 1, -1488, 1737216, -1936036864, 2030351668656, -2106830943512064, 2118312344000340992,...

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

Explicit solution

$A_{n}=\dbinom{3n}{n}\dbinom{6n}{3n}\sum_{k=0}^{n}\dbinom{n}{k}\dbinom{2k}{k}\dbinom{2n-2k}{n-k}$

Maple LaTex

Characteristic classes:

$C_3$	$C_2 H$	$H^3$	$ \vert H \vert$
$-470$	$92$	$8$	$9$

Monodromy (with respect to Frobenius basis)

$1$	$-1$	$\frac{ 1}{ 2}$	$-\frac{ 1}{ 6}$
$0$	$1$	$-1$	$\frac{ 1}{ 2}$
$0$	$0$	$1$	$-1$
$0$	$0$	$0$	$1$

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$1.+2.277630552I$	$0$	$1.091364639I$	$.648450116$
$\frac{ 23}{ 6}$	$1$	$\frac{ 529}{ 288}$	$-1.091364639I$
$0$	$0$	$1$	$0$
$8$	$0$	$\frac{ 23}{ 6}$	$1.-2.277630552I$

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$\frac{ 37}{ 12}+940\lambda$	$-.52083333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-1.138815272I$	$.99826388888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889+2.182729279I$	$1.025632871-1.186265914I$
$\frac{ 23}{ 3}+\frac{ 1}{ 250000000}I$	$-\frac{ 11}{ 12}+\frac{ 3}{ 1000000000}I$	$\frac{ 529}{ 144}-\frac{ 1}{ 250000000}I$	$-.99826388888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889-2.182729279I$
$4+\frac{ 1}{ 500000000}I$	$-1+\frac{ 1}{ 1000000000}I$	$\frac{ 35}{ 12}-\frac{ 1}{ 500000000}I$	$-\frac{ 25}{ 48}-235\lambda$
$16+\frac{ 9}{ 1000000000}I$	$-3.999999988+.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8I$	$\frac{ 23}{ 3}-\frac{ 1}{ 125000000}I$	$-\frac{ 13}{ 12}-940\lambda$

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Basis of the Doran-Morgan lattice

$-\frac{ 284703819}{ 125000000}I$	$\frac{ 31}{ 6}$	$1$	$1$
$-\frac{ 23}{ 6}$	$-4$	$-1$	$0$
$0$	$8$	$0$	$0$
$-8$	$0$	$0$	$0$

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8

New Number: 2.17 | AESZ: 111 | Superseeker: 32 1440 | Hash: d8535e0f3d0bfd4ebcc9c042df43c218

Degree: 2

$\theta^4-2^{4} x(2\theta+1)^2(8\theta^2+8\theta+3)+2^{12} x^{2}(2\theta+1)^2(2\theta+3)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 48, 5904, 940800, 169520400, ...
--> OEIS
Normalized instanton numbers (n₀=1): 32, -96, 1440, 19704, -14496, ... ; Common denominator:...

Discriminant

$(256z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 256}$ $\infty$
$0$ $0$ $\frac{ 1}{ 2}$
$0$ $\frac{ 1}{ 2}$ $\frac{ 1}{ 2}$
$0$ $\frac{ 1}{ 2}$ $\frac{ 3}{ 2}$
$0$ $1$ $\frac{ 3}{ 2}$

\(0\)	\(\frac{ 1}{ 256}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(\frac{ 1}{ 2}\)	\(\frac{ 1}{ 2}\)
\(0\)	\(\frac{ 1}{ 2}\)	\(\frac{ 3}{ 2}\)
\(0\)	\(1\)	\(\frac{ 3}{ 2}\)

Note:

B-Incarnations:
Fibre product 81111- x 18--21, 4*11-- x 53211,
Double Octics: D.O.8, D.O.36, D.O.73, D.O.249, D.O.258,D.O.265

9

New Number: 2.18 | AESZ: 110 | Superseeker: 36 8076 | Hash: 5060b638cac581d5f0f9dd7f40d90e6c

Degree: 2

$\theta^4-2^{2} 3 x(3\theta+1)(3\theta+2)(8\theta^2+8\theta+3)+2^{8} 3^{2} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 72, 14760, 3951360, 1198751400, ...
--> OEIS
Normalized instanton numbers (n₀=1): 36, -144, 8076, -57996, 6960672, ... ; Common denominator:...

Discriminant

$(432z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 432}$ $\infty$
$0$ $0$ $\frac{ 1}{ 3}$
$0$ $\frac{ 1}{ 2}$ $\frac{ 2}{ 3}$
$0$ $\frac{ 1}{ 2}$ $\frac{ 4}{ 3}$
$0$ $1$ $\frac{ 5}{ 3}$

10

New Number: 2.19 | AESZ: 112 | Superseeker: -288 -96055968 | Hash: 9a988f0cb0ca922885043cdadf98dd79

Degree: 2

$\theta^4-2^{4} 3 x(6\theta+1)(6\theta+5)(8\theta^2+8\theta+3)+2^{12} 3^{2} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 720, 2273040, 9605756160, 46308725583120, ...
--> OEIS
Normalized instanton numbers (n₀=1): -288, 162504, -96055968, 106571782296, -135291308081760, ... ; Common denominator:...

Discriminant

$(6912z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 6912}$ $\infty$
$0$ $0$ $\frac{ 1}{ 6}$
$0$ $\frac{ 1}{ 2}$ $\frac{ 5}{ 6}$
$0$ $\frac{ 1}{ 2}$ $\frac{ 7}{ 6}$
$0$ $1$ $\frac{ 11}{ 6}$

11

New Number: 2.1 | AESZ: 45 | Superseeker: 12 3204 | Hash: cdf289f6febf84eb577a238542a57457

Degree: 2

$\theta^4-2^{2} x(2\theta+1)^2(7\theta^2+7\theta+2)-2^{7} x^{2}(2\theta+1)^2(2\theta+3)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 360, 22400, 1695400, ...
--> OEIS
Normalized instanton numbers (n₀=1): 12, 163, 3204, 107582, 4203360, ... ; Common denominator:...

Discriminant

$-(16z+1)(128z-1)$

Local exponents

$-\frac{ 1}{ 16}$ $0$ $\frac{ 1}{ 128}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $\frac{ 3}{ 2}$
$2$ $0$ $2$ $\frac{ 3}{ 2}$

Note:

Hadamard product $A \ast a$, where $A$ is (:case 2.1.1)

12

New Number: 2.20 | AESZ: 133 | Superseeker: 12 -3284/3 | Hash: 4c9628f7dd48f4e9e6ec75303e557389

Degree: 2

$\theta^4-2^{2} 3 x(2\theta+1)^2(3\theta^2+3\theta+1)+2^{4} 3^{3} x^{2}(2\theta+1)^2(2\theta+3)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 12, 324, 8400, 44100, ...
--> OEIS
Normalized instanton numbers (n₀=1): 12, -42, -3284/3, -20538, -103776, ... ; Common denominator:...

Discriminant

$1-144z+6912z^2$

Local exponents

$0$ $\frac{ 1}{ 96}-\frac{ 1}{ 288}\sqrt{ 3}I$ $\frac{ 1}{ 96}+\frac{ 1}{ 288}\sqrt{ 3}I$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $\frac{ 3}{ 2}$
$0$ $2$ $2$ $\frac{ 3}{ 2}$

Note:

Hadamard product A*f
Explicit solution not yet verified

Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 12, -324, -29544, -1314756, -12971988, 2033927928, 146587697352,...
Coefficients of the q-coordinate : 0, 1, -36, 1134, -24912, 564597, -11502648, 173126610,...

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

Explicit solution

$A_{n}=\dbinom{2n}{n}^2\sum_{k=0}^{n}(-1)^{k}3^{n-3k}\dbinom{n}{3k}\frac{(3k)!}{k!^3}$

Maple LaTex

No topological data

Monodromy (with respect to Frobenius basis)

$1$	$-1$	$\frac{ 1}{ 2}$	$-\frac{ 1}{ 6}$
$0$	$1$	$-1$	$\frac{ 1}{ 2}$
$0$	$0$	$1$	$-1$
$0$	$0$	$0$	$1$

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$\frac{ 1}{ 6}+120\lambda$	$-\frac{ 5}{ 36}+20\lambda$	$-\frac{ 5}{ 54}+\frac{ 40}{ 3}\lambda$	$-.9896550e-2+\frac{ 50}{ 9}\lambda$
$4+\frac{ 7}{ 1000000000}I$	$\frac{ 5}{ 3}-\frac{ 1}{ 500000000}I$	$\frac{ 4}{ 9}-\frac{ 1}{ 500000000}I$	$\frac{ 5}{ 54}-\frac{ 40}{ 3}\lambda$
$-6.-.11e-7I$	$-1+\frac{ 3}{ 1000000000}I$	$\frac{ 1}{ 3}+\frac{ 3}{ 1000000000}I$	$-\frac{ 5}{ 36}+20\lambda$
$36.000000031+.67e-7I$	$-24I3^{ \frac{ 19}{ 41}}\lambdaPi^3-\frac{ 1}{ 62500000}I$	$4-\frac{ 9}{ 500000000}I$	$\frac{ 11}{ 6}-120\lambda$

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$\frac{ 11}{ 6}+120\lambda$	$-\frac{ 5}{ 36}-20\lambda$	$\frac{ 5}{ 54}+\frac{ 40}{ 3}\lambda$	$-.9896550e-2-\frac{ 50}{ 9}\lambda$
$4$	$\frac{ 1}{ 3}$	$\frac{ 4}{ 9}$	$-\frac{ 5}{ 54}-\frac{ 40}{ 3}\lambda$
$6$	$-1$	$\frac{ 5}{ 3}$	$-\frac{ 5}{ 36}-20\lambda$
$36$	$-6$	$4$	$\frac{ 1}{ 6}-120\lambda$

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Basis of the Doran-Morgan lattice

$\frac{ 5}{ 6}-120\lambda$	$\frac{ 78000000031}{ 6000000000}+\frac{ 71}{ 3000000000}I$	$\frac{ 302400000483599999147}{ 259200000446400001090}+\frac{ 1124400000899}{ 259200000446400001090}I$	$1$
$-4-\frac{ 7}{ 1000000000}I$	$-\frac{ 48000000031}{ 2000000000}-\frac{ 89}{ 2000000000}I$	$-\frac{ 648000001115999998236}{ 648000001116000002725}-\frac{ 2412000002077}{ 648000001116000002725}I$	$0$
$6+\frac{ 11}{ 1000000000}I$	$\frac{ 36000000031}{ 1000000000}+\frac{ 67}{ 1000000000}I$	$0$	$0$
$-\frac{ 36000000031}{ 1000000000}-\frac{ 67}{ 1000000000}I$	$0$	$0$	$0$

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13

New Number: 2.21 | AESZ: 134 | Superseeker: 18 -5177 | Hash: cc6d92c4b8a8dadb92b447c54e3a2a2f

Degree: 2

$\theta^4-3^{2} x(3\theta+1)(3\theta+2)(3\theta^2+3\theta+1)+3^{5} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 18, 810, 35280, 311850, ...
--> OEIS
Normalized instanton numbers (n₀=1): 18, -207/2, -5177, -155979, -923301, ... ; Common denominator:...

Discriminant

$1-243z+19683z^2$

Local exponents

$0$ $\frac{ 1}{ 162}-\frac{ 1}{ 486}\sqrt{ 3}I$ $\frac{ 1}{ 162}+\frac{ 1}{ 486}\sqrt{ 3}I$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 3}$
$0$ $1$ $1$ $\frac{ 2}{ 3}$
$0$ $1$ $1$ $\frac{ 4}{ 3}$
$0$ $2$ $2$ $\frac{ 5}{ 3}$

Note:

Hadamard product $B\ast f$

Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 18, -810, -139761, -9983466, -115412607, 46702921761, 5144778419274,...
Coefficients of the q-coordinate : 0, 1, -63, 3564, -150735, 6501681, -261382950, 9012994434,...

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

Explicit solution

$A_{n}=\dbinom{2n}{n}\dbinom{3n}{n}\sum_{k=0}^{n}(-1)^{k}3^{n-3k}\dbinom{n}{3k}\frac{(3k)!}{k!^3}$

Maple LaTex

No topological data

Monodromy (with respect to Frobenius basis)

$1$	$-1$	$\frac{ 1}{ 2}$	$-\frac{ 1}{ 6}$
$0$	$1$	$-1$	$\frac{ 1}{ 2}$
$0$	$0$	$1$	$-1$
$0$	$0$	$0$	$1$

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$\frac{ 3}{ 16}+198\lambda$	$-\frac{ 13}{ 96}+33\lambda$	$-\frac{ 143}{ 1152}+\frac{ 121}{ 4}\lambda$	$.9648440e-2+.57748434e-1I$
$\frac{ 33}{ 8}+\frac{ 1}{ 125000000}I$	$\frac{ 27}{ 16}-\frac{ 1}{ 500000000}I$	$\frac{ 121}{ 192}-\frac{ 3}{ 1000000000}I$	$\frac{ 143}{ 1152}-\frac{ 121}{ 4}\lambda$
$-\frac{ 9}{ 2}-\frac{ 9}{ 1000000000}I$	$-\frac{ 3}{ 4}+\frac{ 1}{ 500000000}I$	$\frac{ 5}{ 16}+\frac{ 3}{ 1000000000}I$	$-\frac{ 13}{ 96}+33\lambda$
$27.000000025+.54000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7I$	$4.500000045-.14000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7I$	$\frac{ 33}{ 8}-\frac{ 9}{ 500000000}I$	$\frac{ 29}{ 16}-198\lambda$

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$\frac{ 29}{ 16}+198\lambda$	$-\frac{ 13}{ 96}-33\lambda$	$\frac{ 143}{ 1152}+\frac{ 121}{ 4}\lambda$	$.9648440e-2-.57748434e-1I$
$\frac{ 33}{ 8}$	$\frac{ 5}{ 16}$	$\frac{ 121}{ 192}$	$-\frac{ 143}{ 1152}-\frac{ 121}{ 4}\lambda$
$\frac{ 9}{ 2}$	$-\frac{ 3}{ 4}$	$\frac{ 27}{ 16}$	$-\frac{ 13}{ 96}-33\lambda$
$27$	$-\frac{ 9}{ 2}$	$\frac{ 33}{ 8}$	$\frac{ 3}{ 16}-198\lambda$

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Basis of the Doran-Morgan lattice

$\frac{ 13}{ 16}-198\lambda$	$\frac{ 2610000001}{ 240000000}+\frac{ 43}{ 2000000000}I$	$\frac{ 850500001462499997223}{ 729000001350000003541}+\frac{ 3402000002925}{ 729000001350000003541}I$	$1$
$-\frac{ 33}{ 8}-\frac{ 1}{ 125000000}I$	$-\frac{ 1440000001}{ 80000000}-\frac{ 9}{ 250000000}I$	$-\frac{ 729000001349999997709}{ 729000001350000003541}-\frac{ 2916000002700}{ 729000001350000003541}I$	$0$
$\frac{ 9}{ 2}+\frac{ 9}{ 1000000000}I$	$\frac{ 1080000001}{ 40000000}+\frac{ 27}{ 500000000}I$	$0$	$0$
$-\frac{ 1080000001}{ 40000000}-\frac{ 27}{ 500000000}I$	$0$	$0$	$0$

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14

New Number: 2.22 | AESZ: 135 | Superseeker: 36 -206716/3 | Hash: 85e55291bd94bb32087b43f104c60645

Degree: 2

$\theta^4-2^{2} 3 x(4\theta+1)(4\theta+3)(3\theta^2+3\theta+1)+2^{4} 3^{3} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 36, 3780, 388080, 8108100, ...
--> OEIS
Normalized instanton numbers (n₀=1): 36, -477, -206716/3, -4431924, -27005472, ... ; Common denominator:...

Discriminant

$1-576z+110592z^2$

Local exponents

$0$ $\frac{ 1}{ 384}-\frac{ 1}{ 1152}\sqrt{ 3}I$ $\frac{ 1}{ 384}+\frac{ 1}{ 1152}\sqrt{ 3}I$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 4}$
$0$ $1$ $1$ $\frac{ 3}{ 4}$
$0$ $1$ $1$ $\frac{ 5}{ 4}$
$0$ $2$ $2$ $\frac{ 7}{ 4}$

Integral instantons: Hadamard, product, $C, \ast, f$.,...
Coefficients of the Yukawa coupling: 1, 36, -3780, -1860408, -283646916, -3375683964, 8182006866936, 1873126855818072,...
Coefficients of the q-coordinate : 0, 1, -156, 22446, -2570800, 297228021, -32847734088, 3343576302482,...

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

No topological data

Monodromy (with respect to Frobenius basis)

$1$	$-1$	$\frac{ 1}{ 2}$	$-\frac{ 1}{ 6}$
$0$	$1$	$-1$	$\frac{ 1}{ 2}$
$0$	$0$	$1$	$-1$
$0$	$0$	$0$	$1$

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$\frac{ 5}{ 24}+Itan(\frac{ 801}{ 812})$	$-\frac{ 19}{ 144}+52\lambda$	$-\frac{ 323}{ 1728}+\frac{ 221}{ 3}\lambda$	$.92182440e-1+\frac{ 247}{ 9}\lambda$
$\frac{ 17}{ 4}+\frac{ 9}{ 1000000000}I$	$\frac{ 41}{ 24}-\frac{ 3}{ 1000000000}I$	$\frac{ 289}{ 288}-\frac{ 1}{ 250000000}I$	$\frac{ 323}{ 1728}-\frac{ 221}{ 3}\lambda$
$-3-\frac{ 3}{ 500000000}I$	$-\frac{ 1}{ 2}+\frac{ 1}{ 500000000}I$	$\frac{ 7}{ 24}+\frac{ 3}{ 1000000000}I$	$-\frac{ 19}{ 144}+52\lambda$
$18.000000018+.41e-7I$	$3.000000039-.12000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7I$	$\frac{ 17}{ 4}-\frac{ 9}{ 500000000}I$	$\frac{ 43}{ 24}-Itan(\frac{ 801}{ 812})$

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$\frac{ 43}{ 24}+Itan(\frac{ 801}{ 812})$	$-\frac{ 19}{ 144}-52\lambda$	$\frac{ 323}{ 1728}+\frac{ 221}{ 3}\lambda$	$.92182440e-1-\frac{ 247}{ 9}\lambda$
$\frac{ 17}{ 4}$	$\frac{ 7}{ 24}$	$\frac{ 289}{ 288}$	$-\frac{ 323}{ 1728}-\frac{ 221}{ 3}\lambda$
$3$	$-\frac{ 1}{ 2}$	$\frac{ 41}{ 24}$	$-\frac{ 19}{ 144}-52\lambda$
$18$	$-3$	$\frac{ 17}{ 4}$	$\frac{ 5}{ 24}-Itan(\frac{ 801}{ 812})$

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Basis of the Doran-Morgan lattice

$\frac{ 19}{ 24}-\frac{ 1162393719353719131361189363784404603456366390101814206736549803033200099854000208071729302850101578}{ 768799759549186043811713254203741173211443985818991590275710787225120378790852066470688698366857287}I$	$\frac{ 8750000003}{ 1000000000}+\frac{ 113}{ 6000000000}I$	$\frac{ 378000000701999998397}{ 324000000648000002005}+\frac{ 1707000001584}{ 324000000648000002005}I$	$1$
$-\frac{ 17}{ 4}-\frac{ 9}{ 1000000000}I$	$-\frac{ 12000000009}{ 1000000000}-\frac{ 53}{ 2000000000}I$	$-\frac{ 324000000647999998643}{ 324000000648000002005}-\frac{ 1476000001476}{ 324000000648000002005}I$	$0$
$3+\frac{ 3}{ 500000000}I$	$\frac{ 9000000009}{ 500000000}+\frac{ 41}{ 1000000000}I$	$0$	$0$
$-\frac{ 9000000009}{ 500000000}-\frac{ 41}{ 1000000000}I$	$0$	$0$	$0$

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15

New Number: 2.23 | AESZ: 136 | Superseeker: 180 -21847076 | Hash: ff626c2fb953cb886f45f717a6a98a20

Degree: 2

$\theta^4-2^{2} 3^{2} x(6\theta+1)(6\theta+5)(3\theta^2+3\theta+1)+2^{4} 3^{5} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 180, 124740, 85765680, 12047014980, ...
--> OEIS
Normalized instanton numbers (n₀=1): 180, -15615, -21847076, -7438074210, 255591208800, ... ; Common denominator:...

Discriminant

$1-3888z+5038848z^2$

Local exponents

$0$ $\frac{ 1}{ 2592}-\frac{ 1}{ 7776}\sqrt{ 3}I$ $\frac{ 1}{ 2592}+\frac{ 1}{ 7776}\sqrt{ 3}I$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 6}$
$0$ $1$ $1$ $\frac{ 5}{ 6}$
$0$ $1$ $1$ $\frac{ 7}{ 6}$
$0$ $2$ $2$ $\frac{ 11}{ 6}$

Note:

Hadamard product $D \ast f$

Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 180, -124740, -589870872, -476036874180, 31948901100180, 761206364926270200, 937547029773672579000,...
Coefficients of the q-coordinate : 0, 1, -1116, 1183086, -1060601520, 951553112949, -831445527865032, 696322110834525906,...

	Gopakumar-Vafa invariants
g=0	,...
g=1	,...
g=2	,...

No topological data

Monodromy (with respect to Frobenius basis)

$1$	$-1$	$\frac{ 1}{ 2}$	$-\frac{ 1}{ 6}$
$0$	$1$	$-1$	$\frac{ 1}{ 2}$
$0$	$0$	$1$	$-1$
$0$	$0$	$0$	$1$

copy data

$.22916666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667+2.587775989I$	$-.12847222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222+.431296008I$	$-.374710642+1.257946661I$	$.678044505+.443276440I$
$\frac{ 35}{ 8}+\frac{ 3}{ 250000000}I$	$1.729166682-.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8I$	$\frac{ 1225}{ 576}-\frac{ 1}{ 100000000}I$	$.374710644-Iexp(\frac{ 5}{ 9})ln(2)^{ \frac{ 4}{ 9}}Zeta(5)^(\frac{ 9}{ 2})$
$-\frac{ 3}{ 2}-\frac{ 1}{ 250000000}I$	$-\frac{ 1}{ 4}+\frac{ 1}{ 500000000}I$	$\frac{ 13}{ 48}+\frac{ 3}{ 1000000000}I$	$-\frac{ 37}{ 288}+89\lambda$
$9+\frac{ 1}{ 40000000}I$	$1.500000032-.10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7I$	$\frac{ 35}{ 8}-\frac{ 1}{ 50000000}I$	$1.7708333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-2.587775987I$

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$1.7708333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333+2.587775988I$	$-\frac{ 37}{ 288}-89\lambda$	$.374710648+1.257946661I$	$.678044504-.443276442I$
$\frac{ 35}{ 8}$	$\frac{ 13}{ 48}$	$\frac{ 1225}{ 576}$	$-.374710648-\frac{ 1}{ 5}I3^{ \frac{ 31}{ 39}}5^(\frac{ 3}{ 5})$
$\frac{ 3}{ 2}$	$-\frac{ 1}{ 4}$	$\frac{ 83}{ 48}$	$-\frac{ 37}{ 288}-89\lambda$
$9$	$-\frac{ 3}{ 2}$	$\frac{ 35}{ 8}$	$.22916666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667-2.587775988I$

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Basis of the Doran-Morgan lattice

$\frac{ 37}{ 48}-\frac{ 2587775989}{ 1000000000}I$	$\frac{ 53}{ 8}+\frac{ 109}{ 6000000000}I$	$\frac{ 3779999999999999971}{ 3240000000000000025}+\frac{ 837600000}{ 129600000000000001}I$	$1$
$-\frac{ 35}{ 8}-\frac{ 3}{ 250000000}I$	$-6-\frac{ 33}{ 2000000000}I$	$-\frac{ 129599999999999999}{ 129600000000000001}-\frac{ 720000000}{ 129600000000000001}I$	$0$
$\frac{ 3}{ 2}+\frac{ 1}{ 250000000}I$	$9+\frac{ 1}{ 40000000}I$	$0$	$0$
$-9-\frac{ 1}{ 40000000}I$	$0$	$0$	$0$

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16

New Number: 2.24 | AESZ: 137 | Superseeker: 20 1684/3 | Hash: 198d6c822d6c46225ac2553d60df6539

Degree: 2

$\theta^4-2^{2} x(2\theta+1)^2(17\theta^2+17\theta+6)+2^{7} 3^{2} x^{2}(2\theta+1)^2(2\theta+3)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 24, 1512, 124800, 11730600, ...
--> OEIS
Normalized instanton numbers (n₀=1): 20, 2, 1684/3, 7602, 173472, ... ; Common denominator:...

Discriminant

$(144z-1)(128z-1)$

Local exponents

$0$ $\frac{ 1}{ 144}$ $\frac{ 1}{ 128}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $\frac{ 3}{ 2}$
$0$ $2$ $2$ $\frac{ 3}{ 2}$

Note:

Hadamard product $A \ast g$.

17

New Number: 2.25 | AESZ: 138 | Superseeker: 27 2618 | Hash: c524254b716132352b27914640b03c8b

Degree: 2

$\theta^4-3 x(3\theta+1)(3\theta+2)(17\theta^2+17\theta+6)+2^{3} 3^{4} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 36, 3780, 524160, 82952100, ...
--> OEIS
Normalized instanton numbers (n₀=1): 27, 189/4, 2618, 43713, 2319057, ... ; Common denominator:...

Discriminant

$(243z-1)(216z-1)$

Local exponents

$0$ $\frac{ 1}{ 243}$ $\frac{ 1}{ 216}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 3}$
$0$ $1$ $1$ $\frac{ 2}{ 3}$
$0$ $1$ $1$ $\frac{ 4}{ 3}$
$0$ $2$ $2$ $\frac{ 5}{ 3}$

Note:

Hadamard product $B\ast g$.

18

New Number: 2.26 | AESZ: 139 | Superseeker: 44 22500 | Hash: f5d9215987323abcff6ed8709927af5d

Degree: 2

$\theta^4-2^{2} x(4\theta+1)(4\theta+3)(17\theta^2+17\theta+6)+2^{7} 3^{2} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 72, 17640, 5765760, 2156754600, ...
--> OEIS
Normalized instanton numbers (n₀=1): 44, 607, 22500, 1444678, 128626784, ... ; Common denominator:...

Discriminant

$(576z-1)(512z-1)$

Local exponents

$0$ $\frac{ 1}{ 576}$ $\frac{ 1}{ 512}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 4}$
$0$ $1$ $1$ $\frac{ 3}{ 4}$
$0$ $1$ $1$ $\frac{ 5}{ 4}$
$0$ $2$ $2$ $\frac{ 7}{ 4}$

Note:

Hadamard product $C \ast g$

19

New Number: 2.27 | AESZ: 140 | Superseeker: 108 -4945756 | Hash: 74692097f8183c067c2c4b1a5c93387b

Degree: 2

$\theta^4-2^{2} 3 x(6\theta+1)(6\theta+5)(17\theta^2+17\theta+6)+2^{7} 3^{4} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 360, 582120, 1274232960, 3204505984680, ...
--> OEIS
Normalized instanton numbers (n₀=1): 108, 54135, -4945756, 7925523138, -2434666062240, ... ; Common denominator:...

Discriminant

$(3888z-1)(3456z-1)$

Local exponents

$0$ $\frac{ 1}{ 3888}$ $\frac{ 1}{ 3456}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 6}$
$0$ $1$ $1$ $\frac{ 5}{ 6}$
$0$ $1$ $1$ $\frac{ 7}{ 6}$
$0$ $2$ $2$ $\frac{ 11}{ 6}$

Note:

Hadamard product $D \ast g$

20

New Number: 2.28 | AESZ: 49 | Superseeker: 48 2864 | Hash: 0a357a8c4fd703ab062148eadcd94daa

Degree: 2

$\theta^4-2^{2} 3 x(2\theta+1)^2(18\theta^2+18\theta+7)+2^{4} 3^{6} x^{2}(2\theta+1)^2(2\theta+3)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 84, 17820, 4868400, 1499003100, ...
--> OEIS
Normalized instanton numbers (n₀=1): 48, -438, 2864, 77958, -4942032, ... ; Common denominator:...

Discriminant

$(432z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 432}$ $\infty$
$0$ $0$ $\frac{ 1}{ 2}$
$0$ $\frac{ 1}{ 3}$ $\frac{ 1}{ 2}$
$0$ $\frac{ 2}{ 3}$ $\frac{ 3}{ 2}$
$0$ $1$ $\frac{ 3}{ 2}$

Note:

Hadamard product $A \ast$

21

New Number: 2.29 | AESZ: 142 | Superseeker: 45 27735 | Hash: 85c2c2d8111a859d4cc03e8892c56af9

Degree: 2

$\theta^4-3^{2} x(3\theta+1)(3\theta+2)(18\theta^2+18\theta+7)+3^{8} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 126, 44550, 20447280, 10600093350, ...
--> OEIS
Normalized instanton numbers (n₀=1): 45, -3465/4, 27735, -1156005, 55721970, ... ; Common denominator:...

Discriminant

$(729z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 729}$ $\infty$
$0$ $0$ $\frac{ 1}{ 3}$
$0$ $\frac{ 1}{ 3}$ $\frac{ 2}{ 3}$
$0$ $\frac{ 2}{ 3}$ $\frac{ 4}{ 3}$
$0$ $1$ $\frac{ 5}{ 3}$

Note:

Hadamard product $A \ast$

22

New Number: 2.2 | AESZ: 15 | Superseeker: 21 15894 | Hash: c8053e0e9c05ef468263fafd5e3fc764

Degree: 2

$\theta^4-3 x(3\theta+1)(3\theta+2)(7\theta^2+7\theta+2)-2^{3} 3^{2} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 12, 900, 94080, 11988900, ...
--> OEIS
Normalized instanton numbers (n₀=1): 21, 480, 15894, 894075, 58703151, ... ; Common denominator:...

Discriminant

$-(27z+1)(216z-1)$

Local exponents

$-\frac{ 1}{ 27}$ $0$ $\frac{ 1}{ 216}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 3}$
$1$ $0$ $1$ $\frac{ 2}{ 3}$
$1$ $0$ $1$ $\frac{ 4}{ 3}$
$2$ $0$ $2$ $\frac{ 5}{ 3}$

Note:

Hadamard product $B\ast a$.

A-Incarnation: diagonal of (3,3)-intersection in $P^2 \times P^2$

23

New Number: 2.30 | AESZ: 143 | Superseeker: -1008 -607849200 | Hash: e9217db4c6dcfdb9588bab85e6a5f136

Degree: 2

$\theta^4-2^{2} 3^{2} x(6\theta+1)(6\theta+5)(18\theta^2+18\theta+7)+2^{4} 3^{8} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 1260, 6860700, 49707337680, 409490086185180, ...
--> OEIS
Normalized instanton numbers (n₀=1): -1008, 499086, -607849200, 1097705372526, -2467344815777520, ... ; Common denominator:...

Discriminant

$(11664z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 11664}$ $\infty$
$0$ $0$ $\frac{ 1}{ 6}$
$0$ $\frac{ 1}{ 3}$ $\frac{ 5}{ 6}$
$0$ $\frac{ 2}{ 3}$ $\frac{ 7}{ 6}$
$0$ $1$ $\frac{ 11}{ 6}$

Note:

$D\ast h^{\tilde{\;}}B\ast\kappa$

24

New Number: 2.31 | AESZ: 7** | Superseeker: 96 -12064 | Hash: 2c494088fc85599f73fb344776dbbb28

Degree: 2

$\theta^4-2^{4} x(2\theta+1)^2(32\theta^2+32\theta+13)+2^{16} x^{2}(2\theta+1)^2(2\theta+3)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 208, 107280, 70739200, 52362595600, ...
--> OEIS
Normalized instanton numbers (n₀=1): 96, -3560, -12064, 1941800, -489007584, ... ; Common denominator:...

Discriminant

$(1024z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 1024}$ $\infty$
$0$ $0$ $\frac{ 1}{ 2}$
$0$ $\frac{ 1}{ 4}$ $\frac{ 1}{ 2}$
$0$ $\frac{ 3}{ 4}$ $\frac{ 3}{ 2}$
$0$ $1$ $\frac{ 3}{ 2}$

Note:

This operator replaces AESZ 43, to which it is equivalent.

25

New Number: 2.32 | AESZ: | Superseeker: 60 307860 | Hash: c2f30268af49d0bdc6a36f8b0fce3367

Degree: 2

$\theta^4-2^{2} 3 x(3\theta+1)(3\theta+2)(32\theta^2+32\theta+13)+2^{12} 3^{2} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 312, 268200, 297104640, 370278354600, ...
--> OEIS
Normalized instanton numbers (n₀=1): 60, -7635, 307860, -44194980, 3687387360, ... ; Common denominator:...

Discriminant

$(1728z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 1728}$ $\infty$
$0$ $0$ $\frac{ 1}{ 3}$
$0$ $\frac{ 1}{ 4}$ $\frac{ 2}{ 3}$
$0$ $\frac{ 3}{ 4}$ $\frac{ 4}{ 3}$
$0$ $1$ $\frac{ 5}{ 3}$

Note:

This is operator "2.32" from ...

26

New Number: 2.33 | AESZ: | Superseeker: -160 -539680 | Hash: 83a66e92381baa083f87a13e02375bc9

Degree: 2

$\theta^4-2^{4} x(4\theta+1)(4\theta+3)(32\theta^2+32\theta+13)+2^{16} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 624, 1251600, 3268151040, 9627237219600, ...
--> OEIS
Normalized instanton numbers (n₀=1): -160, -6920, -539680, -54568560, -6402958560, ... ; Common denominator:...

Discriminant

$(4096z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 4096}$ $\infty$
$0$ $0$ $\frac{ 1}{ 4}$
$0$ $\frac{ 1}{ 4}$ $\frac{ 3}{ 4}$
$0$ $\frac{ 3}{ 4}$ $\frac{ 5}{ 4}$
$0$ $1$ $\frac{ 7}{ 4}$

Note:

This is operator "2.33" from ...

27

New Number: 2.34 | AESZ: | Superseeker: -3936 -10892932064 | Hash: 3047f1b969ee26b92708d8eab03c0aed

Degree: 2

$\theta^4-2^{4} 3 x(6\theta+1)(6\theta+5)(32\theta^2+32\theta+13)+2^{16} 3^{2} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 3120, 41302800, 722261379840, 14304149060881680, ...
--> OEIS
Normalized instanton numbers (n₀=1): -3936, 3550992, -10892932064, 48014348072136, -264897451764337440, ... ; Common denominator:...

Discriminant

$(27648z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 27648}$ $\infty$
$0$ $0$ $\frac{ 1}{ 6}$
$0$ $\frac{ 1}{ 4}$ $\frac{ 5}{ 6}$
$0$ $\frac{ 3}{ 4}$ $\frac{ 7}{ 6}$
$0$ $1$ $\frac{ 11}{ 6}$

Note:

This is operator "2.34" from ...

28

New Number: 2.35 | AESZ: ~67 | Superseeker: 480 -16034720 | Hash: f06ee3928cd6d738db065f3f83d12160

Degree: 2

$\theta^4-2^{4} 3 x(2\theta+1)^2(72\theta^2+72\theta+31)+2^{12} 3^{6} x^{2}(2\theta+1)^2(2\theta+3)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 1488, 5351184, 24363091200, 123873273392400, ...
--> OEIS
Normalized instanton numbers (n₀=1): 480, -226968, -16034720, 10943202744, -4352645747040, ... ; Common denominator:...

Discriminant

$(6912z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 6912}$ $\infty$
$0$ $0$ $\frac{ 1}{ 2}$
$0$ $\frac{ 1}{ 6}$ $\frac{ 1}{ 2}$
$0$ $\frac{ 5}{ 6}$ $\frac{ 3}{ 2}$
$0$ $1$ $\frac{ 3}{ 2}$

Note:

This is operator "2.35" from ...

29

New Number: 2.36 | AESZ: | Superseeker: -36 128217204 | Hash: 4dbde07f1392f8d49d0e10858d3a17f1

Degree: 2

$\theta^4-2^{2} 3^{2} x(3\theta+1)(3\theta+2)(72\theta^2+72\theta+31)+2^{8} 3^{8} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 2232, 13377960, 102324983040, 875961004703400, ...
--> OEIS
Normalized instanton numbers (n₀=1): -36, -486279, 128217204, -74772628524, 63925611915744, ... ; Common denominator:...

Discriminant

$(11664z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 11664}$ $\infty$
$0$ $0$ $\frac{ 1}{ 3}$
$0$ $\frac{ 1}{ 6}$ $\frac{ 2}{ 3}$
$0$ $\frac{ 5}{ 6}$ $\frac{ 4}{ 3}$
$0$ $1$ $\frac{ 5}{ 3}$

Note:

This is operator "2.36" from ...

30

New Number: 2.37 | AESZ: | Superseeker: -2592 81451104 | Hash: fb56d2f39692cfb98f66d467355b3c99

Degree: 2

$\theta^4-2^{4} 3 x(4\theta+1)(4\theta+3)(72\theta^2+72\theta+31)+2^{12} 3^{6} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 4464, 62430480, 1125574813440, 22774986122288400, ...
--> OEIS
Normalized instanton numbers (n₀=1): -2592, -307800, 81451104, 144135316512, 98667659422368, ... ; Common denominator:...

Discriminant

$(27648z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 27648}$ $\infty$
$0$ $0$ $\frac{ 1}{ 4}$
$0$ $\frac{ 1}{ 6}$ $\frac{ 3}{ 4}$
$0$ $\frac{ 5}{ 6}$ $\frac{ 5}{ 4}$
$0$ $1$ $\frac{ 7}{ 4}$

Note:

Hadamard product $B\ast c$.

\(4+468\lambda\)	\(-1.-.755979502I\)	\(\frac{ 1}{ 2}+78\lambda\)	\(-.71415832e-1-52\lambda\)
\(9\)	\(-2\)	\(\frac{ 3}{ 2}\)	\(-\frac{ 1}{ 2}-78\lambda\)
\(18\)	\(-6\)	\(4\)	\(-1.-.755979502I\)
\(54\)	\(-18\)	\(9\)	\(-2-468\lambda\)

\(4.+3.256527087I\)	\(-1-224\lambda\)	\(\frac{ 3}{ 4}+168\lambda\)	\(.44582463e-1-112\lambda\)
\(9\)	\(-2\)	\(\frac{ 9}{ 4}\)	\(-\frac{ 3}{ 4}-168\lambda\)
\(12\)	\(-4\)	\(4\)	\(-1-224\lambda\)
\(36\)	\(-12\)	\(9\)	\(-2.-3.256527087I\)

\(4.+5.291856516I\)	\(-1-364\lambda\)	\(\frac{ 3}{ 2}+546\lambda\)	\(1.055763632-364\lambda\)
\(9\)	\(-2\)	\(\frac{ 9}{ 2}\)	\(-\frac{ 3}{ 2}-546\lambda\)
\(6\)	\(-2\)	\(4\)	\(-1-364\lambda\)
\(18\)	\(-6\)	\(9\)	\(-2.-5.291856516I\)

\(\frac{ 10}{ 3}+176\lambda\)	\(-\frac{ 7}{ 12}-44\lambda\)	\(\frac{ 35}{ 144}+\frac{ 55}{ 3}\lambda\)	\(-.73703221e-1-\frac{ 77}{ 6}\lambda\)
\(\frac{ 20}{ 3}+\frac{ 1}{ 500000000}I\)	\(-\frac{ 2}{ 3}+\frac{ 1}{ 1000000000}I\)	\(\frac{ 25}{ 36}\)	\(-\frac{ 35}{ 144}-\frac{ 55}{ 3}\lambda\)
\(16+\frac{ 1}{ 200000000}I\)	\(-4+\frac{ 1}{ 500000000}I\)	\(\frac{ 8}{ 3}-\frac{ 1}{ 500000000}I\)	\(-\frac{ 7}{ 12}-44\lambda\)
\(64.+.23e-7I\)	\(-15.999999981+.90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8I\)	\(\frac{ 20}{ 3}-\frac{ 1}{ 125000000}I\)	\(-\frac{ 4}{ 3}-176\lambda\)

\(\frac{ 13}{ 4}+324\lambda\)	\(-\frac{ 9}{ 16}-81\lambda\)	\(\frac{ 21}{ 64}+\frac{ 189}{ 4}\lambda\)	\(-.54109387e-1-\frac{ 243}{ 8}\lambda\)
\(7+\frac{ 1}{ 500000000}I\)	\(-\frac{ 3}{ 4}+\frac{ 1}{ 1000000000}I\)	\(\frac{ 49}{ 48}-\frac{ 1}{ 1000000000}I\)	\(-\frac{ 21}{ 64}-\frac{ 189}{ 4}\lambda\)
\(12+\frac{ 1}{ 250000000}I\)	\(-3+\frac{ 1}{ 500000000}I\)	\(\frac{ 11}{ 4}-\frac{ 1}{ 500000000}I\)	\(-\frac{ 9}{ 16}-81\lambda\)
\(48.+.19e-7I\)	\(-11.999999983+.80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8I\)	\(7-\frac{ 1}{ 125000000}I\)	\(-\frac{ 5}{ 4}-324\lambda\)

\(1\)	\(-1\)	\(\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 6}\)
\(0\)	\(1\)	\(-1\)	\(\frac{ 1}{ 2}\)
\(0\)	\(0\)	\(1\)	\(-1\)
\(0\)	\(0\)	\(0\)	\(1\)

\(1.+.755979502I\)	\(0\)	\(26\lambda\)	\(.31750278e-1\)
\(3\)	\(1\)	\(\frac{ 1}{ 2}\)	\(-26\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(18\)	\(0\)	\(3\)	\(1.-.755979502I\)

\(-\frac{ 377989751}{ 500000000}I\)	\(6\)	\(1\)	\(1\)
\(-3\)	\(-9\)	\(-1\)	\(0\)
\(0\)	\(18\)	\(0\)	\(0\)
\(-18\)	\(0\)	\(0\)	\(0\)

\(1+224\lambda\)	\(0\)	\(56\lambda\)	\(.98194154e-1\)
\(3\)	\(1\)	\(\frac{ 3}{ 4}\)	\(-56\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(12\)	\(0\)	\(3\)	\(1-224\lambda\)

\(-224\lambda\)	\(5\)	\(1\)	\(1\)
\(-3\)	\(-6\)	\(-1\)	\(0\)
\(0\)	\(12\)	\(0\)	\(0\)
\(-12\)	\(0\)	\(0\)	\(0\)

\(1+364\lambda\)	\(0\)	\(182\lambda\)	\(.518587877\)
\(3\)	\(1\)	\(\frac{ 3}{ 2}\)	\(-182\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(6\)	\(0\)	\(3\)	\(1-364\lambda\)

\(-364\lambda\)	\(4\)	\(1\)	\(1\)
\(-3\)	\(-3\)	\(-1\)	\(0\)
\(0\)	\(6\)	\(0\)	\(0\)
\(-6\)	\(0\)	\(0\)	\(0\)

\(1+88\lambda\)	\(0\)	\(\frac{ 55}{ 6}\lambda\)	\(.5683112e-2\)
\(\frac{ 10}{ 3}\)	\(1\)	\(\frac{ 25}{ 72}\)	\(-\frac{ 55}{ 6}\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(32\)	\(0\)	\(\frac{ 10}{ 3}\)	\(1-88\lambda\)

\(-88\lambda\)	\(\frac{ 26}{ 3}\)	\(1\)	\(1\)
\(-\frac{ 10}{ 3}\)	\(-16\)	\(-1\)	\(0\)
\(0\)	\(32\)	\(0\)	\(0\)
\(-32\)	\(0\)	\(0\)	\(0\)

\(1+162\lambda\)	\(0\)	\(\frac{ 189}{ 8}\lambda\)	\(.25679681e-1\)
\(\frac{ 7}{ 2}\)	\(1\)	\(\frac{ 49}{ 96}\)	\(-\frac{ 189}{ 8}\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(24\)	\(0\)	\(\frac{ 7}{ 2}\)	\(1-162\lambda\)

\(-162\lambda\)	\(\frac{ 15}{ 2}\)	\(1\)	\(1\)
\(-\frac{ 7}{ 2}\)	\(-12\)	\(-1\)	\(0\)
\(0\)	\(24\)	\(0\)	\(0\)
\(-24\)	\(0\)	\(0\)	\(0\)

\(1+268\lambda\)	\(0\)	\(Iarctan(\frac{ 173}{ 564})\)	\(.105419378\)
\(\frac{ 11}{ 3}\)	\(1\)	\(\frac{ 121}{ 144}\)	\(-Iarctan(\frac{ 173}{ 564})\)
\(0\)	\(0\)	\(1\)	\(0\)
\(16\)	\(0\)	\(\frac{ 11}{ 3}\)	\(1-268\lambda\)

\(\frac{ 19}{ 6}+4Iln(2)^{ \frac{ 6}{ 5}}Zeta(5)^(\frac{ 2}{ 9})\)	\(-\frac{ 13}{ 24}-134\lambda\)	\(.49652777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778+.595253091I\)	\(.64137367e-1-.351740463I\)
\(\frac{ 22}{ 3}+\frac{ 3}{ 1000000000}I\)	\(-\frac{ 5}{ 6}+\frac{ 1}{ 500000000}I\)	\(\frac{ 121}{ 72}-\frac{ 1}{ 500000000}I\)	\(-.49652777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778-.595253091I\)
\(8+\frac{ 3}{ 1000000000}I\)	\(-2+\frac{ 1}{ 500000000}I\)	\(\frac{ 17}{ 6}-\frac{ 1}{ 500000000}I\)	\(-\frac{ 13}{ 24}-134\lambda\)
\(32+\frac{ 7}{ 500000000}I\)	\(-8+\frac{ 7}{ 1000000000}I\)	\(\frac{ 22}{ 3}-\frac{ 7}{ 1000000000}I\)	\(-\frac{ 7}{ 6}-4Iln(2)^{ \frac{ 6}{ 5}}Zeta(5)^(\frac{ 2}{ 9})\)

\(-268\lambda\)	\(\frac{ 19}{ 3}\)	\(1\)	\(1\)
\(-\frac{ 11}{ 3}\)	\(-8\)	\(-1\)	\(0\)
\(0\)	\(16\)	\(0\)	\(0\)
\(-16\)	\(0\)	\(0\)	\(0\)

\(1.+2.277630552I\)	\(0\)	\(1.091364639I\)	\(.648450116\)
\(\frac{ 23}{ 6}\)	\(1\)	\(\frac{ 529}{ 288}\)	\(-1.091364639I\)
\(0\)	\(0\)	\(1\)	\(0\)
\(8\)	\(0\)	\(\frac{ 23}{ 6}\)	\(1.-2.277630552I\)

\(\frac{ 37}{ 12}+940\lambda\)	\(-.52083333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-1.138815272I\)	\(.99826388888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889+2.182729279I\)	\(1.025632871-1.186265914I\)
\(\frac{ 23}{ 3}+\frac{ 1}{ 250000000}I\)	\(-\frac{ 11}{ 12}+\frac{ 3}{ 1000000000}I\)	\(\frac{ 529}{ 144}-\frac{ 1}{ 250000000}I\)	\(-.99826388888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889-2.182729279I\)
\(4+\frac{ 1}{ 500000000}I\)	\(-1+\frac{ 1}{ 1000000000}I\)	\(\frac{ 35}{ 12}-\frac{ 1}{ 500000000}I\)	\(-\frac{ 25}{ 48}-235\lambda\)
\(16+\frac{ 9}{ 1000000000}I\)	\(-3.999999988+.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8I\)	\(\frac{ 23}{ 3}-\frac{ 1}{ 125000000}I\)	\(-\frac{ 13}{ 12}-940\lambda\)

\(-\frac{ 284703819}{ 125000000}I\)	\(\frac{ 31}{ 6}\)	\(1\)	\(1\)
\(-\frac{ 23}{ 6}\)	\(-4\)	\(-1\)	\(0\)
\(0\)	\(8\)	\(0\)	\(0\)
\(-8\)	\(0\)	\(0\)	\(0\)

\(-\frac{ 2}{ 3}+96\lambda\)	\(48\lambda\)	\(-\frac{ 5}{ 72}+4\lambda\)	\(-.13526746e-1\)
\(-\frac{ 2}{ 3}\)	\(\frac{ 2}{ 3}\)	\(-\frac{ 1}{ 36}\)	\(-\frac{ 5}{ 72}-4\lambda\)
\(-8\)	\(0\)	\(\frac{ 2}{ 3}\)	\(-48\lambda\)
\(-16\)	\(-8\)	\(-\frac{ 2}{ 3}\)	\(-\frac{ 2}{ 3}-96\lambda\)

\(\frac{ 5}{ 3}-96\lambda\)	\(\frac{ 2}{ 3}\)	\(\frac{ 1}{ 2}\)	\(1\)
\(\frac{ 2}{ 3}\)	\(0\)	\(-1\)	\(0\)
\(8\)	\(-16\)	\(0\)	\(0\)
\(16\)	\(0\)	\(0\)	\(0\)

\(-\frac{ 1}{ 2}+24\lambda\)	\(12\lambda\)	\(-\frac{ 1}{ 8}+2\lambda\)	\(-.1127229e-2\)
\(-1\)	\(\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 12}\)	\(-\frac{ 1}{ 8}-2\lambda\)
\(-6\)	\(0\)	\(\frac{ 1}{ 2}\)	\(-12\lambda\)
\(-12\)	\(-6\)	\(-1\)	\(-\frac{ 1}{ 2}-24\lambda\)

Calabi-Yau differential operator database v.3

Summary

Discriminant

Local exponents

Note:

Explicit solution

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Explicit solution

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Explicit solution

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Explicit solution

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Explicit solution

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Explicit solution

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Explicit solution

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Explicit solution

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Explicit solution

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Explicit solution

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Explicit solution

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Explicit solution

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

\(\frac{ 3}{ 2}-24\lambda\)	\(0\)	\(\frac{ 1}{ 2}\)	\(1\)
\(1\)	\(0\)	\(-1\)	\(0\)
\(6\)	\(-12\)	\(0\)	\(0\)
\(12\)	\(0\)	\(0\)	\(0\)

\(-.16666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667-.969204490I\)	\(-100\lambda\)	\(-\frac{ 35}{ 72}-\frac{ 250}{ 3}\lambda\)	\(-.234839336\)
\(-\frac{ 5}{ 3}\)	\(\frac{ 1}{ 6}\)	\(-\frac{ 25}{ 36}\)	\(-\frac{ 35}{ 72}+\frac{ 250}{ 3}\lambda\)
\(-2\)	\(0\)	\(\frac{ 1}{ 6}\)	\(100\lambda\)
\(-4\)	\(-2\)	\(-\frac{ 5}{ 3}\)	\(-.16666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667+.969204490I\)

\(\frac{ 7}{ 6}+\frac{ 96920449}{ 100000000}I\)	\(-\frac{ 4}{ 3}\)	\(\frac{ 1}{ 2}\)	\(1\)
\(\frac{ 5}{ 3}\)	\(0\)	\(-1\)	\(0\)
\(2\)	\(-4\)	\(0\)	\(0\)
\(4\)	\(0\)	\(0\)	\(0\)

\(4+240\lambda\)	\(-\frac{ 3}{ 2}-120\lambda\)	\(\frac{ 5}{ 8}+50\lambda\)	\(-.159319280-30\lambda\)
\(10\)	\(-4\)	\(\frac{ 25}{ 12}\)	\(-\frac{ 5}{ 8}-50\lambda\)
\(24\)	\(-12\)	\(6\)	\(-\frac{ 3}{ 2}-120\lambda\)
\(48\)	\(-24\)	\(10\)	\(-2-240\lambda\)

\(1+120\lambda\)	\(0\)	\(15\lambda\)	\(.14090360e-1\)
\(3\)	\(1\)	\(\frac{ 3}{ 8}\)	\(-15\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(24\)	\(0\)	\(3\)	\(1-120\lambda\)

\(-120\lambda\)	\(7\)	\(1\)	\(1\)
\(-3\)	\(-12\)	\(-1\)	\(0\)
\(0\)	\(24\)	\(0\)	\(0\)
\(-24\)	\(0\)	\(0\)	\(0\)

\(\frac{ 1}{ 6}+120\lambda\)	\(-\frac{ 5}{ 36}+20\lambda\)	\(-\frac{ 5}{ 54}+\frac{ 40}{ 3}\lambda\)	\(-.9896550e-2+\frac{ 50}{ 9}\lambda\)
\(4+\frac{ 7}{ 1000000000}I\)	\(\frac{ 5}{ 3}-\frac{ 1}{ 500000000}I\)	\(\frac{ 4}{ 9}-\frac{ 1}{ 500000000}I\)	\(\frac{ 5}{ 54}-\frac{ 40}{ 3}\lambda\)
\(-6.-.11e-7I\)	\(-1+\frac{ 3}{ 1000000000}I\)	\(\frac{ 1}{ 3}+\frac{ 3}{ 1000000000}I\)	\(-\frac{ 5}{ 36}+20\lambda\)
\(36.000000031+.67e-7I\)	\(-24I3^{ \frac{ 19}{ 41}}\lambdaPi^3-\frac{ 1}{ 62500000}I\)	\(4-\frac{ 9}{ 500000000}I\)	\(\frac{ 11}{ 6}-120\lambda\)

\(\frac{ 11}{ 6}+120\lambda\)	\(-\frac{ 5}{ 36}-20\lambda\)	\(\frac{ 5}{ 54}+\frac{ 40}{ 3}\lambda\)	\(-.9896550e-2-\frac{ 50}{ 9}\lambda\)
\(4\)	\(\frac{ 1}{ 3}\)	\(\frac{ 4}{ 9}\)	\(-\frac{ 5}{ 54}-\frac{ 40}{ 3}\lambda\)
\(6\)	\(-1\)	\(\frac{ 5}{ 3}\)	\(-\frac{ 5}{ 36}-20\lambda\)
\(36\)	\(-6\)	\(4\)	\(\frac{ 1}{ 6}-120\lambda\)

\(\frac{ 5}{ 6}-120\lambda\)	\(\frac{ 78000000031}{ 6000000000}+\frac{ 71}{ 3000000000}I\)	\(\frac{ 302400000483599999147}{ 259200000446400001090}+\frac{ 1124400000899}{ 259200000446400001090}I\)	\(1\)
\(-4-\frac{ 7}{ 1000000000}I\)	\(-\frac{ 48000000031}{ 2000000000}-\frac{ 89}{ 2000000000}I\)	\(-\frac{ 648000001115999998236}{ 648000001116000002725}-\frac{ 2412000002077}{ 648000001116000002725}I\)	\(0\)
\(6+\frac{ 11}{ 1000000000}I\)	\(\frac{ 36000000031}{ 1000000000}+\frac{ 67}{ 1000000000}I\)	\(0\)	\(0\)
\(-\frac{ 36000000031}{ 1000000000}-\frac{ 67}{ 1000000000}I\)	\(0\)	\(0\)	\(0\)

\(\frac{ 3}{ 16}+198\lambda\)	\(-\frac{ 13}{ 96}+33\lambda\)	\(-\frac{ 143}{ 1152}+\frac{ 121}{ 4}\lambda\)	\(.9648440e-2+.57748434e-1I\)
\(\frac{ 33}{ 8}+\frac{ 1}{ 125000000}I\)	\(\frac{ 27}{ 16}-\frac{ 1}{ 500000000}I\)	\(\frac{ 121}{ 192}-\frac{ 3}{ 1000000000}I\)	\(\frac{ 143}{ 1152}-\frac{ 121}{ 4}\lambda\)
\(-\frac{ 9}{ 2}-\frac{ 9}{ 1000000000}I\)	\(-\frac{ 3}{ 4}+\frac{ 1}{ 500000000}I\)	\(\frac{ 5}{ 16}+\frac{ 3}{ 1000000000}I\)	\(-\frac{ 13}{ 96}+33\lambda\)
\(27.000000025+.54000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7I\)	\(4.500000045-.14000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7I\)	\(\frac{ 33}{ 8}-\frac{ 9}{ 500000000}I\)	\(\frac{ 29}{ 16}-198\lambda\)