Calabi-Yau differential operator database v.3.0

31

New Number: 2.65 | AESZ: 183 | Superseeker: -4 -556/9 | Hash: 04a3788c3f9ed53281ae824deb33d833

Degree: 2

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

Coefficients of the holomorphic solution: 1, -12, 324, -11280, 447300, ...
--> OEIS
Normalized instanton numbers (n₀=1): -4, 8, -556/9, 624, -8928, ... ; Common denominator:...

Discriminant

$(48z+1)(64z+1)$

Local exponents

$-\frac{ 1}{ 48}$ $-\frac{ 1}{ 64}$ $0$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $0$ $\frac{ 3}{ 4}$
$1$ $1$ $0$ $\frac{ 5}{ 4}$
$2$ $2$ $0$ $\frac{ 3}{ 2}$

\(-\frac{ 1}{ 48}\)	\(-\frac{ 1}{ 64}\)	\(0\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(1\)	\(0\)	\(\frac{ 3}{ 4}\)
\(1\)	\(1\)	\(0\)	\(\frac{ 5}{ 4}\)
\(2\)	\(2\)	\(0\)	\(\frac{ 3}{ 2}\)

Note:

This is operator "2.65" from ...

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

32

New Number: 2.69 | AESZ: 205 | Superseeker: 1 5 | Hash: 4fb2e7002e630237d0458c3985cd6a18

Degree: 2

$\theta^4-x\left(59\theta^4+118\theta^3+105\theta^2+46\theta+8\right)+2^{5} 3 x^{2}(\theta+1)^2(3\theta+2)(3\theta+4)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8, 120, 2240, 46840, ...
--> OEIS
Normalized instanton numbers (n₀=1): 1, 7/4, 5, 24, 759/5, ... ; Common denominator:...

Discriminant

$(32z-1)(27z-1)$

Local exponents

$0$ $\frac{ 1}{ 32}$ $\frac{ 1}{ 27}$ $\infty$
$0$ $0$ $0$ $\frac{ 2}{ 3}$
$0$ $1$ $1$ $1$
$0$ $1$ $1$ $1$
$0$ $2$ $2$ $\frac{ 4}{ 3}$

\(0\)	\(\frac{ 1}{ 32}\)	\(\frac{ 1}{ 27}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 2}{ 3}\)
\(0\)	\(1\)	\(1\)	\(1\)
\(0\)	\(1\)	\(1\)	\(1\)
\(0\)	\(2\)	\(2\)	\(\frac{ 4}{ 3}\)

Note:

This is operator "2.69" from ...

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-128\)	\(160\)	\(160\)	\(40\)

33

New Number: 2.6 | AESZ: 24 | Superseeker: 36 41421 | Hash: 5e8f8f32b5e99693a2956e1240b9fdff

Degree: 2

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 18, 1710, 246960, 43347150, ...
--> OEIS
Normalized instanton numbers (n₀=1): 36, 837, 41421, 2992851, 266362506, ... ; Common denominator:...

Discriminant

$1-297z-729z^2$

Local exponents

$-\frac{ 11}{ 54}-\frac{ 5}{ 54}\sqrt{ 5}$ $0$ $-\frac{ 11}{ 54}+\frac{ 5}{ 54}\sqrt{ 5}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 3}$
$1$ $0$ $1$ $\frac{ 2}{ 3}$
$1$ $0$ $1$ $\frac{ 4}{ 3}$
$2$ $0$ $2$ $\frac{ 5}{ 3}$

\(-\frac{ 11}{ 54}-\frac{ 5}{ 54}\sqrt{ 5}\)	\(0\)	\(-\frac{ 11}{ 54}+\frac{ 5}{ 54}\sqrt{ 5}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 3}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 2}{ 3}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 4}{ 3}\)
\(2\)	\(0\)	\(2\)	\(\frac{ 5}{ 3}\)

Note:

Hadamard product B*b
Related to 7.19, 8.18
This operator corresponds to $(Grass(2,5)\vert 1,1,3)_{-150}$ from arXiv:0802.2908

	Gopakumar-Vafa invariants
g=0	540, 12555, 621315, 44892765, 3995437590, 406684089360, 45426958360155, 5432556927598425,...
g=1	0, 0, -1, 13095, 17230617, 6648808835, 1831575868830, 433375127634753,...
g=2	,...

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-150\)	\(66\)	\(15\)	\(8\)

34

New Number: 2.7 | AESZ: 51 | Superseeker: 92 585396 | Hash: e09b9b149b6845daa8d5ef03df33f22d

Degree: 2

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 36, 7980, 2716560, 1127025900, ...
--> OEIS
Normalized instanton numbers (n₀=1): 92, 5052, 585396, 99982012, 21054159152, ... ; Common denominator:...

Discriminant

$1-704z-4096z^2$

Local exponents

$-\frac{ 11}{ 128}-\frac{ 5}{ 128}\sqrt{ 5}$ $0$ $-\frac{ 11}{ 128}+\frac{ 5}{ 128}\sqrt{ 5}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 4}$
$1$ $0$ $1$ $\frac{ 3}{ 4}$
$1$ $0$ $1$ $\frac{ 5}{ 4}$
$2$ $0$ $2$ $\frac{ 7}{ 4}$

\(-\frac{ 11}{ 128}-\frac{ 5}{ 128}\sqrt{ 5}\)	\(0\)	\(-\frac{ 11}{ 128}+\frac{ 5}{ 128}\sqrt{ 5}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 4}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 3}{ 4}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 5}{ 4}\)
\(2\)	\(0\)	\(2\)	\(\frac{ 7}{ 4}\)

Note:

Hadamard product C*b
Related to 8.139
A-Incarnation: double cover of $B_5$.

A:Incarnation: double cover of B

Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 92, 40508, 15805784, 6398889276, 2631769894092, 1095690103233560, 460102352983654760,...
Coefficients of the q-coordinate : 0, 1, -180, 9766, -918864, -84667391, -28201300344, -8416763367758,...

	Gopakumar-Vafa invariants
g=0	920, 50520, 5853960, 999820120, 210541591520, 50726392934600, 13414062769202760, 3797984131204286040,...
g=1	0, 3, -1840, 340009, 1947267584, 1647668876313, 1015529214081408, 546679951529049217,...
g=2	,...

Explicit solution

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

Maple LaTex

Characteristic classes:

$C_3$	$C_2 H$	$H^3$	$ \vert H \vert$
$-200$	$64$	$10$	$7$

Monodromy (with respect to Frobenius basis)

$5.6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667+3.876817960I$	$-2.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-1.938408980I$	$\frac{ 133}{ 90}+\frac{ 760}{ 3}\lambda$	$-.168701507-.904590857I$
$\frac{ 38}{ 3}$	$-\frac{ 16}{ 3}$	$\frac{ 361}{ 90}$	$-\frac{ 133}{ 90}-\frac{ 760}{ 3}\lambda$
$20$	$-10$	$\frac{ 22}{ 3}$	$-2.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-1.938408980I$
$40$	$-20$	$\frac{ 38}{ 3}$	$-3.6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667-3.876817960I$

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

copy data

$1.+.969204490I$	$0$	$\frac{ 160}{ 3}\lambda$	$.93935734e-1$
$\frac{ 8}{ 3}$	$1$	$\frac{ 32}{ 45}$	$-\frac{ 160}{ 3}\lambda$
$0$	$0$	$1$	$0$
$10$	$0$	$\frac{ 8}{ 3}$	$1.-.969204490I$

copy data

Basis of the Doran-Morgan lattice

$-\frac{ 96920449}{ 100000000}I$	$\frac{ 13}{ 3}$	$1$	$1$
$-\frac{ 8}{ 3}$	$-5$	$-1$	$0$
$0$	$10$	$0$	$0$
$-10$	$0$	$0$	$0$

copy data

35

New Number: 2.9 | AESZ: 58 | Superseeker: 16 11056/3 | Hash: 1ca6d3d1c4514db0651efce420265f5a

Degree: 2

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

Maple LaTex

Coefficients of the holomorphic solution: 1, 12, 540, 37200, 3131100, ...
--> OEIS
Normalized instanton numbers (n₀=1): 16, 142, 11056/3, 121470, 4971792, ... ; Common denominator:...

Discriminant

$(144z-1)(16z-1)$

Local exponents

$0$ $\frac{ 1}{ 144}$ $\frac{ 1}{ 16}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $\frac{ 1}{ 2}$
$0$ $1$ $1$ $\frac{ 3}{ 2}$
$0$ $2$ $2$ $\frac{ 3}{ 2}$

\(0\)	\(\frac{ 1}{ 144}\)	\(\frac{ 1}{ 16}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 3}{ 2}\)
\(0\)	\(2\)	\(2\)	\(\frac{ 3}{ 2}\)

Note:

Hadamard product A*c

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-112\)	\(72\)	\(24\)	\(10\)

36

New Number: 3.10 | AESZ: ~103 | Superseeker: 10 664 | Hash: 9239615e8ac132ca232c13367a39ae3b

Degree: 3

$\theta^4-2 x\left(86\theta^4+172\theta^3+143\theta^2+57\theta+9\right)+2^{2} 3^{2} x^{2}(\theta+1)^2(236\theta^2+472\theta+187)-2^{4} 3^{4} 5^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 18, 630, 28980, 1593270, ...
--> OEIS
Normalized instanton numbers (n₀=1): 10, 24, 664, 9088, 234388, ... ; Common denominator:...

Discriminant

$-(100z-1)(-1+36z)^2$

Local exponents

$0$ $\frac{ 1}{ 100}$ $\frac{ 1}{ 36}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $\frac{ 1}{ 2}$ $1$
$0$ $1$ $\frac{ 1}{ 2}$ $2$
$0$ $2$ $1$ $\frac{ 5}{ 2}$

\(0\)	\(\frac{ 1}{ 100}\)	\(\frac{ 1}{ 36}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(0\)	\(1\)	\(\frac{ 1}{ 2}\)	\(1\)
\(0\)	\(1\)	\(\frac{ 1}{ 2}\)	\(2\)
\(0\)	\(2\)	\(1\)	\(\frac{ 5}{ 2}\)

Note:

Operator equivalent to AESZ 103 =$c \ast c$.

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-48\)	\(72\)	\(36\)	\(12\)

37

New Number: 3.12 | AESZ: | Superseeker: 252 1162036 | Hash: baa148eb1a5a05a0d9aca4c78be26905

Degree: 3

$\theta^4-2^{2} 3^{2} x\left(132\theta^4+216\theta^3+165\theta^2+57\theta+7\right)+2^{4} 3^{6} x^{2}(4\theta+3)(160\theta^3+408\theta^2+316\theta+57)-2^{8} 3^{10} x^{3}(4\theta+1)(4\theta+3)(4\theta+7)(4\theta+9)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 252, 202500, 212132880, 251548748100, ...
--> OEIS
Normalized instanton numbers (n₀=1): 252, -19512, 1162036, -91851948, 24209298720, ... ; Common denominator:...

Discriminant

$-(1296z-1)(-1+1728z)^2$

Local exponents

$0$ $\frac{ 1}{ 1728}$ $\frac{ 1}{ 1296}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 4}$
$0$ $\frac{ 1}{ 2}$ $1$ $\frac{ 3}{ 4}$
$0$ $1$ $1$ $\frac{ 7}{ 4}$
$0$ $\frac{ 3}{ 2}$ $2$ $\frac{ 9}{ 4}$

\(0\)	\(\frac{ 1}{ 1728}\)	\(\frac{ 1}{ 1296}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 4}\)
\(0\)	\(\frac{ 1}{ 2}\)	\(1\)	\(\frac{ 3}{ 4}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 7}{ 4}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(2\)	\(\frac{ 9}{ 4}\)

Note:

Operator equivalent to AESZ 154

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

38

New Number: 3.13 | AESZ: | Superseeker: 352 15001120/3 | Hash: b5a6f76d274395537de2c3169fdac9bf

Degree: 3

$\theta^4-2^{2} x\left(688\theta^4+1232\theta^3+902\theta^2+286\theta+33\right)+2^{4} 3^{2} x^{2}(4\theta+3)(3776\theta^3+10096\theta^2+8268\theta+1515)-2^{10} 3^{4} 5^{2} x^{3}(4\theta+1)(4\theta+3)(4\theta+7)(4\theta+9)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 132, 62748, 43686384, 37830871260, ...
--> OEIS
Normalized instanton numbers (n₀=1): 352, 18676, 15001120/3, 1489325052, 586526654304, ... ; Common denominator:...

Discriminant

$-(1600z-1)(-1+576z)^2$

Local exponents

$0$ $\frac{ 1}{ 1600}$ $\frac{ 1}{ 576}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 4}$
$0$ $1$ $\frac{ 1}{ 2}$ $\frac{ 3}{ 4}$
$0$ $1$ $1$ $\frac{ 7}{ 4}$
$0$ $2$ $\frac{ 3}{ 2}$ $\frac{ 9}{ 4}$

\(0\)	\(\frac{ 1}{ 1600}\)	\(\frac{ 1}{ 576}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 4}\)
\(0\)	\(1\)	\(\frac{ 1}{ 2}\)	\(\frac{ 3}{ 4}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 7}{ 4}\)
\(0\)	\(2\)	\(\frac{ 3}{ 2}\)	\(\frac{ 9}{ 4}\)

Note:

Operator equivalent to AESZ 229

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-56\)	\(36\)	\(6\)	\(4\)

39

New Number: 3.14 | AESZ: | Superseeker: 444 19050964 | Hash: dc96aa2da269d989ee90c49dab6a9c5a

Degree: 3

$\theta^4-2^{2} x\left(452\theta^4+920\theta^3+633\theta^2+173\theta+17\right)-2^{4} x^{2}(4\theta+3)(3808\theta^3+10504\theta^2+8884\theta+1635)-2^{8} 11^{2} x^{3}(4\theta+1)(4\theta+3)(4\theta+7)(4\theta+9)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 68, 42220, 38866320, 43812369900, ...
--> OEIS
Normalized instanton numbers (n₀=1): 444, 57104, 19050964, 9432910668, 5781274591408, ... ; Common denominator:...

Discriminant

$-(1936z-1)(1+64z)^2$

Local exponents

$-\frac{ 1}{ 64}$ $0$ $\frac{ 1}{ 1936}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 4}$
$\frac{ 1}{ 2}$ $0$ $1$ $\frac{ 3}{ 4}$
$1$ $0$ $1$ $\frac{ 7}{ 4}$
$\frac{ 3}{ 2}$ $0$ $2$ $\frac{ 9}{ 4}$

\(-\frac{ 1}{ 64}\)	\(0\)	\(\frac{ 1}{ 1936}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 4}\)
\(\frac{ 1}{ 2}\)	\(0\)	\(1\)	\(\frac{ 3}{ 4}\)
\(1\)	\(0\)	\(1\)	\(\frac{ 7}{ 4}\)
\(\frac{ 3}{ 2}\)	\(0\)	\(2\)	\(\frac{ 9}{ 4}\)

Note:

This is operator Pi = 3.14 (approx.), equivalent to AESZ 238.

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-100\)	\(38\)	\(5\)	\(4\)

40

New Number: 3.15 | AESZ: | Superseeker: -32 -16288 | Hash: e21c92d8f9a2222be40fdc71ea51ee35

Degree: 3

$\theta^4+2^{3} x\left(21\theta^4+42\theta^3+30\theta^2+9\theta+1\right)-2^{6} x^{2}(\theta+1)^2(96\theta^2+192\theta+77)+2^{9} 5^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, -8, 720, -68480, 8123920, ...
--> OEIS
Normalized instanton numbers (n₀=1): -32, 468, -16288, 1681645/2, -53608288, ... ; Common denominator:...

Discriminant

$(200z+1)(-1+16z)^2$

Local exponents

$-\frac{ 1}{ 200}$ $0$ $\frac{ 1}{ 16}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $0$ $\frac{ 1}{ 6}$ $1$
$1$ $0$ $\frac{ 5}{ 6}$ $2$
$2$ $0$ $1$ $\frac{ 5}{ 2}$

\(-\frac{ 1}{ 200}\)	\(0\)	\(\frac{ 1}{ 16}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 1}{ 2}\)
\(1\)	\(0\)	\(\frac{ 1}{ 6}\)	\(1\)
\(1\)	\(0\)	\(\frac{ 5}{ 6}\)	\(2\)
\(2\)	\(0\)	\(1\)	\(\frac{ 5}{ 2}\)

Note:

Operator equivalent to AESZ 328

41

New Number: 3.16 | AESZ: 386 | Superseeker: 10 18328 | Hash: 7d032616d3bd41272e22a4d23747d7a0

Degree: 3

$\theta^4-2 x\left(422\theta^4+844\theta^3+751\theta^2+329\theta+57\right)+2^{2} 3^{4} x^{2}(\theta+1)^2(716\theta^2+1432\theta+579)-2^{4} 3^{8} 7^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 114, 22518, 5236980, 1321024950, ...
--> OEIS
Normalized instanton numbers (n₀=1): 10, -872, 18328, -432528, 13706388, ... ; Common denominator:...

Discriminant

$-(196z-1)(-1+324z)^2$

Local exponents

$0$ $\frac{ 1}{ 324}$ $\frac{ 1}{ 196}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $0$ $1$ $1$
$0$ $1$ $1$ $2$
$0$ $1$ $2$ $\frac{ 5}{ 2}$

42

New Number: 3.17 | AESZ: 387 | Superseeker: 68 125636/3 | Hash: 06864aab02693f4b84eb494138bb3428

Degree: 3

$\theta^4-2^{2} x\left(228\theta^4+456\theta^3+385\theta^2+157\theta+26\right)+2^{11} x^{2}(\theta+1)^2(132\theta^2+264\theta+109)-2^{18} 5^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 104, 18600, 3925760, 906368680, ...
--> OEIS
Normalized instanton numbers (n₀=1): 68, 204, 125636/3, 841384, 123715360, ... ; Common denominator:...

Discriminant

$-(400z-1)(-1+256z)^2$

Local exponents

$0$ $\frac{ 1}{ 400}$ $\frac{ 1}{ 256}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $0$ $1$
$0$ $1$ $1$ $2$
$0$ $2$ $1$ $\frac{ 5}{ 2}$

Note:

This is operator "3.17" from ...

43

New Number: 3.18 | AESZ: 388 | Superseeker: 266 11433160/3 | Hash: 7e11db69c1b7bd8781e54a5eadb0e307

Degree: 3

$\theta^4-2 x\left(582\theta^4+1164\theta^3+815\theta^2+233\theta+25\right)+2^{2} x^{2}(\theta+1)^2(2316\theta^2+4632\theta+1907)-2^{4} 17^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 50, 17142, 9383540, 6301530550, ...
--> OEIS
Normalized instanton numbers (n₀=1): 266, 19320, 11433160/3, 1106069392, 397606861972, ... ; Common denominator:...

Discriminant

$-(1156z-1)(4z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 1156}$ $\frac{ 1}{ 4}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $0$ $1$
$0$ $1$ $1$ $2$
$0$ $2$ $1$ $\frac{ 5}{ 2}$

Note:

This is operator "3.18" from ...

44

New Number: 3.1 | AESZ: 34 | Superseeker: 1 28/3 | Hash: e5461c5f5ae4d929328f66b8955a31f5

Degree: 3

$\theta^4-x\left(35\theta^4+70\theta^3+63\theta^2+28\theta+5\right)+x^{2}(\theta+1)^2(259\theta^2+518\theta+285)-3^{2} 5^{2} x^{3}(\theta+1)^2(\theta+2)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, 5, 45, 545, 7885, ...
--> OEIS
Normalized instanton numbers (n₀=1): 1, 2, 28/3, 52, 350, ... ; Common denominator:...

Discriminant

$-(z-1)(25z-1)(9z-1)$

Local exponents

$0$ $\frac{ 1}{ 25}$ $\frac{ 1}{ 9}$ $1$ $\infty$
$0$ $0$ $0$ $0$ $1$
$0$ $1$ $1$ $1$ $1$
$0$ $1$ $1$ $1$ $2$
$0$ $2$ $2$ $2$ $2$

45

New Number: 3.20 | AESZ: 390 | Superseeker: 19 4455 | Hash: cd8ca8746f3610e70893770a090533f9

Degree: 3

$\theta^4-x\left(561\theta^4+1122\theta^3+975\theta^2+414\theta+70\right)+2^{2} 7^{2} x^{2}(\theta+1)^2(534\theta^2+1068\theta+433)-2^{2} 7^{4} 13^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 70, 8442, 1192660, 182057050, ...
--> OEIS
Normalized instanton numbers (n₀=1): 19, -276, 4455, -104648, 2969383, ... ; Common denominator:...

Discriminant

$-(169z-1)(-1+196z)^2$

Local exponents

$0$ $\frac{ 1}{ 196}$ $\frac{ 1}{ 169}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $\frac{ 1}{ 6}$ $1$ $1$
$0$ $\frac{ 5}{ 6}$ $1$ $2$
$0$ $1$ $2$ $\frac{ 5}{ 2}$

Note:

This is operator "3.20" from ...

46

New Number: 3.22 | AESZ: 392 | Superseeker: 166 1016100 | Hash: 5862be5cc4d3ec1686e6b9a6ec08f7e7

Degree: 3

$\theta^4-2 x\left(230\theta^4+496\theta^3+323\theta^2+75\theta+6\right)-2^{2} 3 x^{2}(6\theta+5)(1866\theta^3+5341\theta^2+4760\theta+1084)-2^{4} 3^{2} 13^{2} x^{3}(6\theta+5)(6\theta+11)(3\theta+1)(3\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 12, 5760, 1664544, 681014880, ...
--> OEIS
Normalized instanton numbers (n₀=1): 166, 8076, 1016100, 189329096, 43879949258, ... ; Common denominator:...

Discriminant

$-(676z-1)(1+108z)^2$

Local exponents

$-\frac{ 1}{ 108}$ $0$ $\frac{ 1}{ 676}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 3}$
$\frac{ 1}{ 3}$ $0$ $1$ $\frac{ 5}{ 6}$
$1$ $0$ $1$ $\frac{ 11}{ 6}$
$\frac{ 4}{ 3}$ $0$ $2$ $\frac{ 7}{ 3}$

Note:

This is operator "3.22" from ...

47

New Number: 3.11 | AESZ: | Superseeker: 37 15270 | Hash: e7db0935aa1b331d8fb696a009d2d7bb

Degree: 3

$\theta^4-x\left(865\theta^4+1730\theta^3+1501\theta^2+636\theta+108\right)+2^{5} 3^{2} x^{2}(\theta+1)^2(866\theta^2+1732\theta+709)-2^{8} 3^{4} 17^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 108, 19908, 4278240, 990152100, ...
--> OEIS
Normalized instanton numbers (n₀=1): 37, -570, 15270, -529994, 21300463, ... ; Common denominator:...

Discriminant

$-(289z-1)(-1+288z)^2$

Local exponents

$0$ $\frac{ 1}{ 289}$ $\frac{ 1}{ 288}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $\frac{ 1}{ 2}$ $1$
$0$ $1$ $\frac{ 1}{ 2}$ $2$
$0$ $2$ $1$ $\frac{ 5}{ 2}$

Note:

Operator equivalent to AESZ 144=c \ast c$

48

New Number: 3.19 | AESZ: 389 | Superseeker: 66 69048 | Hash: c5cca5b7bfc61c4e8b38fab025244078

Degree: 3

$\theta^4-2 x\left(742\theta^4+1484\theta^3+1295\theta^2+553\theta+95\right)+2^{2} 5^{3} x^{2}(\theta+1)^2(1468\theta^2+2936\theta+1211)-2^{4} 5^{6} 11^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 190, 61170, 22892500, 9212271250, ...
--> OEIS
Normalized instanton numbers (n₀=1): 66, -1780, 69048, -3847892, 244783420, ... ; Common denominator:...

Discriminant

$-(484z-1)(-1+500z)^2$

Local exponents

$0$ $\frac{ 1}{ 500}$ $\frac{ 1}{ 484}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $0$ $1$ $1$
$0$ $1$ $1$ $2$
$0$ $1$ $2$ $\frac{ 5}{ 2}$

Note:

This is operator "3.19" from ...

49

New Number: 3.21 | AESZ: 391 | Superseeker: 964 85888580/3 | Hash: 907f1fbd0b6f7c89689fb136ee18482a

Degree: 3

$\theta^4-2^{2} x\left(3460\theta^4+5768\theta^3+4385\theta^2+1501\theta+186\right)+2^{10} 3^{2} x^{2}(4\theta+3)(1732\theta^3+4475\theta^2+3531\theta+645)-2^{14} 3^{4} 17^{2} x^{3}(4\theta+1)(4\theta+3)(4\theta+7)(4\theta+9)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 744, 1731240, 5192436480, 17479541356200, ...
--> OEIS
Normalized instanton numbers (n₀=1): 964, -111140, 85888580/3, -9197858184, 3544241969952, ... ; Common denominator:...

Discriminant

$-(4624z-1)(-1+4608z)^2$

Local exponents

$0$ $\frac{ 1}{ 4624}$ $\frac{ 1}{ 4608}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 4}$
$0$ $1$ $\frac{ 1}{ 2}$ $\frac{ 3}{ 4}$
$0$ $1$ $1$ $\frac{ 7}{ 4}$
$0$ $2$ $\frac{ 3}{ 2}$ $\frac{ 9}{ 4}$

Note:

This is operator "3.21" from ...

50

New Number: 3.23 | AESZ: 393 | Superseeker: -128 -263808 | Hash: c49c1e5d127755611021be0fc2c55d06

Degree: 3

$\theta^4+2^{5} x\left(79\theta^4+140\theta^3+112\theta^2+42\theta+6\right)+2^{8} 3 x^{2}(6\theta+5)(462\theta^3+1255\theta^2+1052\theta+235)+2^{13} 3^{2} 5^{2} x^{3}(6\theta+5)(6\theta+11)(3\theta+1)(3\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, -192, 89136, -51502080, 32954034960, ...
--> OEIS
Normalized instanton numbers (n₀=1): -128, -5148, -263808, -22378134, -2164448640, ... ; Common denominator:...

Discriminant

$(800z+1)(1+864z)^2$

Local exponents

$-\frac{ 1}{ 800}$ $-\frac{ 1}{ 864}$ $0$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 3}$
$1$ $\frac{ 1}{ 3}$ $0$ $\frac{ 5}{ 6}$
$1$ $1$ $0$ $\frac{ 11}{ 6}$
$2$ $\frac{ 4}{ 3}$ $0$ $\frac{ 7}{ 3}$

Note:

This is operator "3.23" from ...

51

New Number: 3.24 | AESZ: | Superseeker: -2 -108 | Hash: 3c89cc2017daa2eba88c016b8ae5865c

Degree: 3

$\theta^4+2 x(2\theta+1)^2(3\theta^2+3\theta+1)-2^{2} x^{2}(2\theta+1)(2\theta+3)(47\theta^2+94\theta+51)+2^{4} 7 x^{3}(2\theta+1)(2\theta+3)^2(2\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, -2, 54, -980, 26950, ...
--> OEIS
Normalized instanton numbers (n₀=1): -2, 17, -108, 1498, -19630, ... ; Common denominator:...

Discriminant

$(16z-1)(112z^2-40z-1)$

Local exponents

$\frac{ 5}{ 28}-\frac{ 1}{ 7}\sqrt{ 2}$ $0$ $\frac{ 1}{ 16}$ $\frac{ 5}{ 28}+\frac{ 1}{ 7}\sqrt{ 2}$ $\infty$
$0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $0$ $1$ $1$ $\frac{ 3}{ 2}$
$1$ $0$ $1$ $1$ $\frac{ 3}{ 2}$
$2$ $0$ $2$ $2$ $\frac{ 5}{ 2}$

Note:

This is operator $\tilde{C_9}$

52

New Number: 3.25 | AESZ: | Superseeker: -2 -308/3 | Hash: 287da3a26b0da679d81da411b46958d1

Degree: 3

$\theta^4+2 x(2\theta+1)^2(7\theta^2+7\theta+3)+2^{2} x^{2}(2\theta+1)(2\theta+3)(29\theta^2+58\theta+33)+2^{4} 3 5 x^{3}(2\theta+1)(2\theta+3)^2(2\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, -6, 90, -2100, 59850, ...
--> OEIS
Normalized instanton numbers (n₀=1): -2, 12, -308/3, 1058, -71158/5, ... ; Common denominator:...

Discriminant

$(48z+1)(80z^2+8z+1)$

Local exponents

$-\frac{ 1}{ 20}-\frac{ 1}{ 10}I$ $-\frac{ 1}{ 20}+\frac{ 1}{ 10}I$ $-\frac{ 1}{ 48}$ $0$ $\infty$
$0$ $0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $1$ $1$ $0$ $\frac{ 3}{ 2}$
$1$ $1$ $1$ $0$ $\frac{ 3}{ 2}$
$2$ $2$ $2$ $0$ $\frac{ 5}{ 2}$

Note:

This is operator $\tilde{C_17}$

53

New Number: 3.26 | AESZ: 407 | Superseeker: 2 440 | Hash: c46d32ba4b3738ba34fe1e6c16e6f242

Degree: 3

$\theta^4+2 x\left(132\theta^4+264\theta^3+293\theta^2+161\theta+35\right)+2^{2} 5^{2} x^{2}(\theta+1)^2(228\theta^2+456\theta+335)+2^{6} 5^{4} x^{3}(\theta+1)(\theta+2)(4\theta+5)(4\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, -70, 5650, -484900, 43071250, ...
--> OEIS
Normalized instanton numbers (n₀=1): 2, -44, 440, -4844, 46268, ... ; Common denominator:...

Discriminant

$(64z+1)(1+100z)^2$

Local exponents

$-\frac{ 1}{ 64}$ $-\frac{ 1}{ 100}$ $0$ $\infty$
$0$ $0$ $0$ $1$
$1$ $-\frac{ 1}{ 2}$ $0$ $\frac{ 5}{ 4}$
$1$ $1$ $0$ $\frac{ 7}{ 4}$
$2$ $\frac{ 3}{ 2}$ $0$ $2$

Note:

This is operator "3.26" from ...

54

New Number: 3.27 | AESZ: 408 | Superseeker: -60 -61780 | Hash: 32ab77c73baf49023973ad11e5d0852e

Degree: 3

$\theta^4-2^{2} x(2\theta+1)(46\theta^3+53\theta^2+45\theta+11)-2^{4} x^{2}(8\theta+7)(64\theta^3+312\theta^2+440\theta+135)+2^{8} 3^{2} x^{3}(8\theta+3)(8\theta+7)(8\theta+15)(8\theta+19)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 44, 6060, 972720, 182017260, ...
--> OEIS
Normalized instanton numbers (n₀=1): -60, 975, -61780, 4166460, -1853578608/5, ... ; Common denominator:...

Discriminant

$(144z+1)(-1+256z)^2$

Local exponents

$-\frac{ 1}{ 144}$ $0$ $\frac{ 1}{ 256}$ $\infty$
$0$ $0$ $0$ $\frac{ 3}{ 8}$
$1$ $0$ $\frac{ 1}{ 4}$ $\frac{ 7}{ 8}$
$1$ $0$ $1$ $\frac{ 15}{ 8}$
$2$ $0$ $\frac{ 5}{ 4}$ $\frac{ 19}{ 8}$

Note:

This is operator "3.27" from ...

55

New Number: 3.28 | AESZ: 410 | Superseeker: 7 1057/3 | Hash: accbbff67291992dfbc89e78f5a3c897

Degree: 3

$\theta^4-x\left(145\theta^4+242\theta^3+199\theta^2+78\theta+12\right)+2^{3} x^{2}(2\theta+1)(4\theta+3)(97\theta^2+182\theta+114)-2^{4} 3^{4} x^{3}(2\theta+1)(2\theta+3)(4\theta+3)(4\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 12, 336, 12880, 592200, ...
--> OEIS
Normalized instanton numbers (n₀=1): 7, 22, 1057/3, 5460, 108241, ... ; Common denominator:...

Discriminant

$-(81z-1)(-1+32z)^2$

Local exponents

$0$ $\frac{ 1}{ 81}$ $\frac{ 1}{ 32}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $\frac{ 3}{ 4}$ $\frac{ 3}{ 4}$
$0$ $1$ $1$ $\frac{ 3}{ 2}$
$0$ $2$ $\frac{ 7}{ 4}$ $\frac{ 7}{ 4}$

Note:

This is operator "3.28" from ...

56

New Number: 3.29 | AESZ: 411 | Superseeker: 3 237 | Hash: 767c4e8d5a7bc53fbbd0d49797e65358

Degree: 3

$\theta^4-x\left(16+98\theta+235\theta^2+274\theta^3+145\theta^4\right)+2^{3} x^{2}(2\theta+1)(4\theta+5)(97\theta^2+190\theta+120)-2^{4} 3^{4} x^{3}(4\theta+5)(2\theta+3)(2\theta+1)(4\theta+9)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 16, 468, 17520, 774060, ...
--> OEIS
Normalized instanton numbers (n₀=1): 3, 36, 237, 4638, 72330, ... ; Common denominator:...

Discriminant

$-(81z-1)(-1+32z)^2$

Local exponents

$0$ $\frac{ 1}{ 81}$ $\frac{ 1}{ 32}$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$0$ $1$ $\frac{ 1}{ 4}$ $\frac{ 5}{ 4}$
$0$ $1$ $1$ $\frac{ 3}{ 2}$
$0$ $2$ $\frac{ 5}{ 4}$ $\frac{ 9}{ 4}$

Note:

This is operator "3.29" from ...

57

New Number: 3.2 | AESZ: 227 | Superseeker: -900 8364884 | Hash: 2e00a51fe0c232d13a452380f44c79da

Degree: 3

$\theta^4+2^{2} 3^{2} x\left(132\theta^4+264\theta^3+201\theta^2+69\theta+10\right)+2^{9} 3^{6} x^{2}\left(20\theta^4+80\theta^3+107\theta^2+54\theta+10\right)+2^{12} 3^{10} x^{3}(2\theta+5)^2(2\theta+1)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, -360, 314280, -348076800, 431342188200, ...
--> OEIS
Normalized instanton numbers (n₀=1): -900, -27387, 8364884, 2066389488, -208833104160, ... ; Common denominator:...

Discriminant

$(1296z+1)(1+1728z)^2$

Local exponents

$-\frac{ 1}{ 1296}$ $-\frac{ 1}{ 1728}$ $0$ $\infty$
$0$ $0$ $0$ $\frac{ 1}{ 2}$
$1$ $\frac{ 1}{ 2}$ $0$ $\frac{ 1}{ 2}$
$1$ $\frac{ 1}{ 2}$ $0$ $\frac{ 5}{ 2}$
$2$ $1$ $0$ $\frac{ 5}{ 2}$

58

New Number: 3.30 | AESZ: 422 | Superseeker: 124 2152276/9 | Hash: b37ac82ae57415849cb59beac4cd6adf

Degree: 3

$\theta^4+2^{2} x\left(380\theta^4+760\theta^3+907\theta^2+527\theta+117\right)+2^{4} 3 x^{2}(8\theta+7)(8\theta+9)(184\theta^2+368\theta+183)-2^{8} 3^{2} x^{3}(8\theta+7)(8\theta+9)(8\theta+15)(8\theta+17)$

Maple LaTex

Coefficients of the holomorphic solution: 1, -468, 280260, -182276400, 123566444100, ...
--> OEIS
Normalized instanton numbers (n₀=1): 124, -3752, 2152276/9, -18042588, 1647569184, ... ; Common denominator:...

Discriminant

$-(16z-1)(1+768z)^2$

Local exponents

$-\frac{ 1}{ 768}$ $0$ $\frac{ 1}{ 16}$ $\infty$
$0$ $0$ $0$ $\frac{ 7}{ 8}$
$-\frac{ 1}{ 2}$ $0$ $1$ $\frac{ 9}{ 8}$
$1$ $0$ $1$ $\frac{ 15}{ 8}$
$\frac{ 3}{ 2}$ $0$ $2$ $\frac{ 17}{ 8}$

Note:

This is operator "3.30" from ...

59

New Number: 3.32 | AESZ: | Superseeker: 128 382592 | Hash: 9b39b616939718654c472dbfb37cdd4e

Degree: 3

$\theta^4-2^{4} x(6\theta^2+6\theta-1)(2\theta+1)^2-2^{10} x^{2}(60\theta^2+120\theta+97)(\theta+1)^2-2^{21} x^{3}(\theta+1)^2(\theta+2)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, -16, 4624, 678656, 238896400, ...
--> OEIS
Normalized instanton numbers (n₀=1): 128, 4084, 382592, 51510860, 8644861312, ... ; Common denominator:...

Discriminant

$-(512z-1)(1+64z)^2$

Local exponents

$-\frac{ 1}{ 64}$ $0$ $\frac{ 1}{ 512}$ $\infty$
$0$ $0$ $0$ $1$
$-\frac{ 1}{ 2}$ $0$ $1$ $1$
$1$ $0$ $1$ $2$
$\frac{ 3}{ 2}$ $0$ $2$ $2$

Note:

Operator equivalent to AESZ 220
B-Incarnation:
Double octic:D.O.244

60

New Number: 3.33 | AESZ: | Superseeker: 4 1580/9 | Hash: da01a7b2dfcebe6e332be6c29ed2a8e5

Degree: 3

$\theta^4+2^{2} x\left(36\theta^4+72\theta^3+85\theta^2+49\theta+11\right)+2^{4} x^{2}(8\theta^2+16\theta+11)(48\theta^2+96\theta+49)+2^{8} x^{3}(4\theta+7)^2(4\theta+5)^2$

Maple LaTex

Coefficients of the holomorphic solution: 1, -44, 2244, -122576, 6952516, ...
--> OEIS
Normalized instanton numbers (n₀=1): 4, -25, 1580/9, -1580, 17120, ... ; Common denominator:...

Discriminant

$(16z+1)(1+64z)^2$

Local exponents

$-\frac{ 1}{ 16}$ $-\frac{ 1}{ 64}$ $0$ $\infty$
$0$ $0$ $0$ $\frac{ 5}{ 4}$
$1$ $-\frac{ 1}{ 2}$ $0$ $\frac{ 5}{ 4}$
$1$ $1$ $0$ $\frac{ 7}{ 4}$
$2$ $\frac{ 3}{ 2}$ $0$ $\frac{ 7}{ 4}$

Note:

Operator equivalent to AESZ 353

\(3.666666992+1.240581667I\)	\(-.888889273-.413527825I\)	\(.296296213+.137842738I\)	\(-.38694844e-1-.45947515e-1I\)
\(16.000002509-.2845e-5I\)	\(-4.333336913-.1390e-5I\)	\(1.777778225+.1587e-5I\)	\(-.296296073-.137842774I\)
\(48.000008758-.8909e-5I\)	\(-16.000011149-.4045e-5I\)	\(6.333334810+.4721e-5I\)	\(-.888888245-.413528325I\)
\(144.000033661-.28975e-4I\)	\(-48.000035910-.11385e-4I\)	\(16.000005252+.13912e-4I\)	\(-1.666664890-1.240584998I\)

\(5.+.620290874I\)	\(-2-64\lambda\)	\(\frac{ 7}{ 9}+\frac{ 224}{ 9}\lambda\)	\(-.216878323-.68921208e-1I\)
\(14\)	\(-6\)	\(\frac{ 49}{ 18}\)	\(-\frac{ 7}{ 9}-\frac{ 224}{ 9}\lambda\)
\(36\)	\(-18\)	\(8\)	\(-2-64\lambda\)
\(72\)	\(-36\)	\(14\)	\(-3.-.620290874I\)

\(3.333327178+1.235680918I\)	\(-.293785798-.155290034I\)	\(.97173439e-1+.52174089e-1I\)	\(-.12126753e-1-.18089273e-1I\)
\(13.327492354-.18865422e-1I\)	\(-.677351606+.3680160e-2I\)	\(.556724039+.2392839e-2I\)	\(-.96900942e-1-.51907518e-1I\)
\(39.969803488-.74697659e-1I\)	\(-5.030457990+.13317419e-1I\)	\(2.669647034+\frac{ 1}{ 243}IPi^{ \frac{ 1}{ 6}}Zeta(5)^7\)	\(-.290681436-.15554156171284634760705289672544080604534005037783375314861460957178841309823677581863979848866498740554156171284634760705289672544080604534005037783375314861460957178841309823677581863979848866498741I\)
\(319.859816505-.452770130I\)	\(-40.256438534+.88323845e-1I\)	\(13.361376945+.57428145e-1I\)	\(-1.325622606-1.245780435I\)

\(\frac{ 11}{ 2}+600\lambda\)	\(-\frac{ 9}{ 4}-300\lambda\)	\(\frac{ 21}{ 20}+140\lambda\)	\(-.196596398-90\lambda\)
\(14\)	\(-6\)	\(\frac{ 49}{ 15}\)	\(-\frac{ 21}{ 20}-140\lambda\)
\(30\)	\(-15\)	\(8\)	\(-\frac{ 9}{ 4}-300\lambda\)
\(60\)	\(-30\)	\(14\)	\(-\frac{ 7}{ 2}-600\lambda\)

\(5.6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667+3.876817960I\)	\(-2.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-1.938408980I\)	\(\frac{ 133}{ 90}+\frac{ 760}{ 3}\lambda\)	\(-.168701507-.904590857I\)
\(\frac{ 38}{ 3}\)	\(-\frac{ 16}{ 3}\)	\(\frac{ 361}{ 90}\)	\(-\frac{ 133}{ 90}-\frac{ 760}{ 3}\lambda\)
\(20\)	\(-10\)	\(\frac{ 22}{ 3}\)	\(-2.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-1.938408980I\)
\(40\)	\(-20\)	\(\frac{ 38}{ 3}\)	\(-3.6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667-3.876817960I\)

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

\(-4-\frac{ 310145437}{ 500000000}I\)	\(8\)	\(\frac{ 1}{ 2}\)	\(1\)
\(-14\)	\(0\)	\(-1\)	\(0\)
\(-36\)	\(72\)	\(0\)	\(0\)
\(-72\)	\(0\)	\(0\)	\(0\)

\(1.+.620290874I\)	\(0\)	\(\frac{ 16}{ 3}\lambda\)	\(.2404755e-2\)
\(\frac{ 20}{ 3}\)	\(1\)	\(\frac{ 5}{ 18}\)	\(-\frac{ 16}{ 3}\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(160\)	\(0\)	\(\frac{ 20}{ 3}\)	\(1.-.620290874I\)

\(-\frac{ 310145437}{ 500000000}I\)	\(\frac{ 100}{ 3}\)	\(1\)	\(1\)
\(-\frac{ 20}{ 3}\)	\(-80\)	\(-1\)	\(0\)
\(0\)	\(160\)	\(0\)	\(0\)
\(-160\)	\(0\)	\(0\)	\(0\)

\(1+150\lambda\)	\(0\)	\(\frac{ 55}{ 2}\lambda\)	\(.35225900e-1\)
\(\frac{ 11}{ 4}\)	\(1\)	\(\frac{ 121}{ 240}\)	\(-\frac{ 55}{ 2}\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(15\)	\(0\)	\(\frac{ 11}{ 4}\)	\(1-150\lambda\)

\(-150\lambda\)	\(\frac{ 21}{ 4}\)	\(1\)	\(1\)
\(-\frac{ 11}{ 4}\)	\(-\frac{ 15}{ 2}\)	\(-1\)	\(0\)
\(0\)	\(15\)	\(0\)	\(0\)
\(-15\)	\(0\)	\(0\)	\(0\)

\(1.+.969204490I\)	\(0\)	\(\frac{ 160}{ 3}\lambda\)	\(.93935734e-1\)
\(\frac{ 8}{ 3}\)	\(1\)	\(\frac{ 32}{ 45}\)	\(-\frac{ 160}{ 3}\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(10\)	\(0\)	\(\frac{ 8}{ 3}\)	\(1.-.969204490I\)

\(-\frac{ 96920449}{ 100000000}I\)	\(\frac{ 13}{ 3}\)	\(1\)	\(1\)
\(-\frac{ 8}{ 3}\)	\(-5\)	\(-1\)	\(0\)
\(0\)	\(10\)	\(0\)	\(0\)
\(-10\)	\(0\)	\(0\)	\(0\)

\(1+112\lambda\)	\(0\)	\(14\lambda\)	\(.12274269e-1\)
\(3\)	\(1\)	\(\frac{ 3}{ 8}\)	\(-14\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(24\)	\(0\)	\(3\)	\(1-112\lambda\)

\(4.+1.628263543I\)	\(-1-112\lambda\)	\(\frac{ 3}{ 8}+42\lambda\)	\(-.88177192e-1-28\lambda\)
\(9\)	\(-2\)	\(\frac{ 9}{ 8}\)	\(-\frac{ 3}{ 8}-42\lambda\)
\(24\)	\(-8\)	\(4\)	\(-1-112\lambda\)
\(72\)	\(-24\)	\(9\)	\(-2.-1.628263543I\)

\(-112\lambda\)	\(7\)	\(1\)	\(1\)
\(-3\)	\(-12\)	\(-1\)	\(0\)
\(0\)	\(24\)	\(0\)	\(0\)
\(-24\)	\(0\)	\(0\)	\(0\)

\(-48\lambda\)	\(9\)	\(1\)	\(1\)
\(-3\)	\(-18\)	\(-1\)	\(0\)
\(0\)	\(36\)	\(0\)	\(0\)
\(-36\)	\(0\)	\(0\)	\(0\)

\(12I\lambda+1\)	\(0+\frac{ 7}{ 4}I\)	\(-1\)	\(1\)
\(-\frac{ 1}{ 4}I\)	\(-\frac{ 9}{ 2}I\)	\(1\)	\(0\)
\(0\)	\(0+9I\)	\(0\)	\(0\)
\(-9I\)	\(0\)	\(0\)	\(0\)

\(-56\lambda\)	\(\frac{ 5}{ 2}\)	\(1\)	\(1\)
\(-\frac{ 3}{ 2}\)	\(-3\)	\(-1\)	\(0\)
\(0\)	\(6\)	\(0\)	\(0\)
\(-6\)	\(0\)	\(0\)	\(0\)

\(-100\lambda\)	\(\frac{ 29}{ 12}\)	\(1\)	\(1\)
\(-\frac{ 19}{ 12}\)	\(-\frac{ 5}{ 2}\)	\(-1\)	\(0\)
\(0\)	\(5\)	\(0\)	\(0\)
\(-5\)	\(0\)	\(0\)	\(0\)

\(-\frac{ 17}{ 12}-58\lambda\)	\(\frac{ 17}{ 6}\)	\(\frac{ 1}{ 2}\)	\(1\)
\(-\frac{ 25}{ 6}\)	\(0\)	\(-1\)	\(0\)
\(-8\)	\(16\)	\(0\)	\(0\)
\(-16\)	\(0\)	\(0\)	\(0\)

\(-144\lambda\)	\(-\frac{ 3}{ 2}\)	\(1\)	\(1\)
\(-\frac{ 3}{ 2}\)	\(9\)	\(-1\)	\(0\)
\(0\)	\(-18\)	\(0\)	\(0\)
\(18\)	\(0\)	\(0\)	\(0\)

\(80\lambda\)	\(3\)	\(1\)	\(1\)
\(-1\)	\(-6\)	\(-1\)	\(0\)
\(0\)	\(12\)	\(0\)	\(0\)
\(-12\)	\(0\)	\(0\)	\(0\)

\(-64\lambda\)	\(\frac{ 5}{ 2}\)	\(1\)	\(1\)
\(-\frac{ 3}{ 2}\)	\(-3\)	\(-1\)	\(0\)
\(0\)	\(6\)	\(0\)	\(0\)
\(-6\)	\(0\)	\(0\)	\(0\)

\(-80\lambda\)	\(25\)	\(1\)	\(1\)
\(-5\)	\(-60\)	\(-1\)	\(0\)
\(0\)	\(120\)	\(0\)	\(0\)
\(-120\)	\(0\)	\(0\)	\(0\)

Calabi-Yau differential operator database v.3

Summary

Discriminant

Local exponents

Note:

Explicit solution

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

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:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

Local exponents

Note:

Characteristic classes:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

\(\frac{ 7}{ 12}-224\lambda\)	\(-\frac{ 49}{ 12}\)	\(\frac{ 6}{ 7}\)	\(1\)
\(-\frac{ 7}{ 12}\)	\(\frac{ 35}{ 2}\)	\(-1\)	\(0\)
\(7\)	\(-49\)	\(0\)	\(0\)
\(49\)	\(0\)	\(0\)	\(0\)

\(-36\lambda\)	\(\frac{ 31}{ 12}\)	\(1\)	\(1\)
\(-\frac{ 17}{ 12}\)	\(-\frac{ 7}{ 2}\)	\(-1\)	\(0\)
\(0\)	\(7\)	\(0\)	\(0\)
\(-7\)	\(0\)	\(0\)	\(0\)