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: 2.14 | 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

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

3

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

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

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

4

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

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

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

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)

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

copy data

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

copy data

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

copy data

Basis of the Doran-Morgan lattice

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

copy data

5

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

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

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

Note:

Hadamard product $B\ast g$.

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-156\)	\(108\)	\(36\)	\(15\)

6

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

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

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

Note:

Hadamard product $A \ast$

7

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

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

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

Note:

Hadamard product $B\ast a$.

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

\(C_3\)	\(C_2 H\)	\(H^3\)	\( \vert H \vert\)
\(-162\)	\(72\)	\(18\)	\(9\)

8

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

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

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

Note:

This is operator "2.32" from ...

9

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

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

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

Note:

This is operator "2.36" from ...

10

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

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

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

11

New Number: 5.101 | AESZ: 348 | Superseeker: -52 -44772 | Hash: 8759f016475d17d0fc88f4b98a374d3f

Degree: 5

$\theta^4+2^{2} x\left(70\theta^4+194\theta^3+145\theta^2+48\theta+6\right)-2^{4} 3 x^{2}\left(141\theta^4-858\theta^3-2111\theta^2-1192\theta-206\right)-2^{8} 3^{2} x^{3}\left(18\theta^4-324\theta^3-2364\theta^2-1953\theta-403\right)-2^{10} 3^{4} x^{4}(3\theta+1)(3\theta+2)(42\theta^2+258\theta+223)+2^{14} 3^{6} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, -24, 2160, -309120, 54608400, ...
--> OEIS
Normalized instanton numbers (n₀=1): -52, 461/2, -44772, 3546761/2, -178670332, ... ; Common denominator:...

Discriminant

$(746496z^3+17280z^2+352z+1)(-1+36z)^2$

Local exponents

≈$-0.009925-0.017537I$ ≈$-0.009925+0.017537I$ ≈$-0.003299$ $0$ $\frac{ 1}{ 36}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 3}$
$1$ $1$ $1$ $0$ $1$ $\frac{ 2}{ 3}$
$1$ $1$ $1$ $0$ $3$ $\frac{ 4}{ 3}$
$2$ $2$ $2$ $0$ $4$ $\frac{ 5}{ 3}$

Note:

This is operator "5.101" from ...

12

New Number: 5.103 | AESZ: 354 | Superseeker: 25 17175 | Hash: 0d4263e8c85dceb5c51f8614f7c1bc79

Degree: 5

$\theta^4-5 x\left(170\theta^4+160\theta^3+125\theta^2+45\theta+6\right)+3 5^{3} x^{2}\left(725\theta^4+1220\theta^3+1105\theta^2+460\theta+68\right)-3^{2} 5^{5} x^{3}\left(1421\theta^4+3186\theta^3+3053\theta^2+1272\theta+188\right)+2^{2} 3^{3} 5^{7} x^{4}(3\theta+1)(3\theta+2)(34\theta^2+61\theta+36)-2^{2} 3^{4} 5^{9} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 30, 3150, 462000, 78828750, ...
--> OEIS
Normalized instanton numbers (n₀=1): 25, 2175/4, 17175, 351250, 23000351/5, ... ; Common denominator:...

Discriminant

$-(2278125z^3-84375z^2+550z-1)(-1+150z)^2$

Local exponents

$0$ ≈$0.003863-0.000232I$ ≈$0.003863+0.000232I$ $\frac{ 1}{ 150}$ ≈$0.029311$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 3}$
$0$ $1$ $1$ $1$ $1$ $\frac{ 2}{ 3}$
$0$ $1$ $1$ $3$ $1$ $\frac{ 4}{ 3}$
$0$ $2$ $2$ $4$ $2$ $\frac{ 5}{ 3}$

Note:

This is operator "5.103" from ...

13

New Number: 5.126 | AESZ: | Superseeker: 110 729096 | Hash: 511069e41e6328e47a1ea996049096b4

Degree: 5

$\theta^4-x\left(881\theta^4+1222\theta^3+878\theta^2+267\theta+30\right)+3 x^{2}\left(50601\theta^4+60024\theta^3+17189\theta^2+280\theta-340\right)-3^{2} 5 x^{3}\left(195867\theta^4+207846\theta^3+142719\theta^2+49068\theta+6316\right)+2^{2} 3^{4} 5^{2} x^{4}(3\theta+1)(3\theta+2)(1902\theta^2+1767\theta+386)+2^{2} 3^{6} 5^{4} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 30, 6210, 2004240, 789638850, ...
--> OEIS
Normalized instanton numbers (n₀=1): 110, 12935/2, 729096, 247828991/2, 26419290920, ... ; Common denominator:...

Discriminant

$(675z-1)(27z-1)(z+1)(-1+90z)^2$

Local exponents

$-1$ $0$ $\frac{ 1}{ 675}$ $\frac{ 1}{ 90}$ $\frac{ 1}{ 27}$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 3}$
$1$ $0$ $1$ $1$ $1$ $\frac{ 2}{ 3}$
$1$ $0$ $1$ $3$ $1$ $\frac{ 4}{ 3}$
$2$ $0$ $2$ $4$ $2$ $\frac{ 5}{ 3}$

Note:

Operator London 18.
B-Incarnation: Laurent-polynomial.

14

New Number: 5.127 | AESZ: | Superseeker: 957/10 1581774/5 | Hash: 8b1c933faa73767af598d82d1e214624

Degree: 5

$2^{2} 5^{2} \theta^4-2 3 5 x\left(1812\theta^4+3858\theta^3+2799\theta^2+870\theta+100\right)-3 x^{2}\left(293697\theta^4-124614\theta^3-930203\theta^2-562390\theta-95700\right)+3^{3} x^{3}\left(62631\theta^4+977400\theta^3+677140\theta^2+104550\theta-6300\right)+3^{5} 5 13 x^{4}(3\theta+1)(3\theta+2)(308\theta^2-16\theta-231)-3^{8} 13^{2} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 30, 5130, 1369200, 446603850, ...
--> OEIS
Normalized instanton numbers (n₀=1): 957/10, 32493/10, 1581774/5, 423123141/10, 14142369903/2, ... ; Common denominator:...

Discriminant

$-(6561z^3-4320z^2+567z-1)(10+117z)^2$

Local exponents

$-\frac{ 10}{ 117}$ $0$ ≈$0.001788$ ≈$0.178154$ ≈$0.478494$ $\infty$
$0$ $0$ $0$ $0$ $0$ $\frac{ 1}{ 3}$
$1$ $0$ $1$ $1$ $1$ $\frac{ 2}{ 3}$
$3$ $0$ $1$ $1$ $1$ $\frac{ 4}{ 3}$
$4$ $0$ $2$ $2$ $2$ $\frac{ 5}{ 3}$

Note:

Operator London 9.
B-Incarnation as Laurent-polynomial.

15

New Number: 5.19 | AESZ: 180 | Superseeker: -624 -43406256 | Hash: c174fb2dfd87730e48b4ae8b57ac66df

Degree: 5

$\theta^4-2^{4} 3 x\left(198\theta^4+72\theta^3+69\theta^2+33\theta+5\right)+2^{9} 3^{2} x^{2}\left(7614\theta^4+7128\theta^3+6813\theta^2+2529\theta+340\right)-2^{14} 3^{5} x^{3}\left(15714\theta^4+27216\theta^3+26343\theta^2+11151\theta+1685\right)+2^{19} 3^{9} x^{4}(3\theta+1)(3\theta+2)(576\theta^2+1008\theta+605)-2^{27} 3^{13} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 240, 173520, 170016000, 193451504400, ...
--> OEIS
Normalized instanton numbers (n₀=1): -624, -137190, -43406256, -18281817141, -9083828410320, ... ; Common denominator:...

Discriminant

$-(-1+864z)(2592z-1)^2(1728z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 2592}$ $\frac{ 1}{ 1728}$ $\frac{ 1}{ 864}$ $\infty$
$0$ $0$ $0$ $0$ $\frac{ 1}{ 3}$
$0$ $1$ $\frac{ 1}{ 2}$ $1$ $\frac{ 2}{ 3}$
$0$ $3$ $\frac{ 1}{ 2}$ $1$ $\frac{ 4}{ 3}$
$0$ $4$ $1$ $2$ $\frac{ 5}{ 3}$

Note:

This is operator "5.19" from ...

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

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

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

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

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

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

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

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

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

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

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

\(1.+.755979502I\)	\(0\)	\(\frac{ 39}{ 2}\lambda\)	\(.15875139e-1\)
\(\frac{ 9}{ 2}\)	\(1\)	\(\frac{ 9}{ 16}\)	\(-\frac{ 39}{ 2}\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(36\)	\(0\)	\(\frac{ 9}{ 2}\)	\(1.-.755979502I\)

\(.84386396e-1+.881341465I\)	\(-.593907697+1.816219110I\)	\(.987405021+.251865740I\)	\(-.18197034e-1-.280246794I\)
\(-.610146073+4.105015738I\)	\(3.086102688+5.881005017I\)	\(\frac{ 1}{ ln}(2)^{ \frac{ 8}{ 3}}ln(3)^{ \frac{ 8}{ 5}}Zeta(5)^8-1.317777791I\)	\(-.605925748-.688412508I\)
\(-1.084750363+4.722447485I\)	\(1.891556916+7.035664131I\)	\(4.676916900-1.255046419I\)	\(-.642466556-.856579334I\)
\(-4.881168587+32.840125900I\)	\(16.688821505+47.048040140I\)	\(24.445126799-10.542222328I\)	\(-3.847405984-5.507300063I\)

\(-\frac{ 377989751}{ 500000000}I\)	\(\frac{ 21}{ 2}\)	\(1\)	\(1\)
\(-\frac{ 9}{ 2}\)	\(-18\)	\(-1\)	\(0\)
\(0\)	\(36\)	\(0\)	\(0\)
\(-36\)	\(0\)	\(0\)	\(0\)

\(-\frac{ 5}{ 16}+90\lambda\)	\(\frac{ 7}{ 32}+45\lambda\)	\(-\frac{ 7}{ 128}+\frac{ 15}{ 4}\lambda\)	\(.42666543e-1\)
\(-\frac{ 3}{ 8}\)	\(\frac{ 13}{ 16}\)	\(-\frac{ 1}{ 64}\)	\(-\frac{ 7}{ 128}-\frac{ 15}{ 4}\lambda\)
\(-\frac{ 9}{ 2}\)	\(\frac{ 3}{ 4}\)	\(\frac{ 13}{ 16}\)	\(\frac{ 7}{ 32}-45\lambda\)
\(-9\)	\(-\frac{ 9}{ 2}\)	\(-\frac{ 3}{ 8}\)	\(-\frac{ 5}{ 16}-90\lambda\)

\(\frac{ 21}{ 16}-90\lambda\)	\(\frac{ 3}{ 8}\)	\(\frac{ 1}{ 2}\)	\(1\)
\(\frac{ 3}{ 8}\)	\(0\)	\(-1\)	\(0\)
\(\frac{ 9}{ 2}\)	\(-9\)	\(0\)	\(0\)
\(9\)	\(0\)	\(0\)	\(0\)

\(4+324\lambda\)	\(-\frac{ 3}{ 2}-162\lambda\)	\(\frac{ 3}{ 4}+81\lambda\)	\(-\frac{ 222}{ 1223}-54\lambda\)
\(9\)	\(-\frac{ 7}{ 2}\)	\(\frac{ 9}{ 4}\)	\(-\frac{ 3}{ 4}-81\lambda\)
\(18\)	\(-9\)	\(\frac{ 11}{ 2}\)	\(-\frac{ 3}{ 2}-162\lambda\)
\(36\)	\(-18\)	\(9\)	\(-2-324\lambda\)

\(1+162\lambda\)	\(0\)	\(27\lambda\)	\(.34239575e-1\)
\(3\)	\(1\)	\(\frac{ 1}{ 2}\)	\(-27\lambda\)
\(0\)	\(0\)	\(1\)	\(0\)
\(18\)	\(0\)	\(3\)	\(1-162\lambda\)

\(-.12500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+.872284041I\)	\(\frac{ 9}{ 16}+90\lambda\)	\(\frac{ 3}{ 64}-\frac{ 15}{ 2}\lambda\)	\(.84124259e-1\)
\(\frac{ 1}{ 4}\)	\(\frac{ 9}{ 8}\)	\(-\frac{ 1}{ 96}\)	\(\frac{ 3}{ 64}+\frac{ 15}{ 2}\lambda\)
\(-3\)	\(\frac{ 3}{ 2}\)	\(\frac{ 9}{ 8}\)	\(\frac{ 9}{ 16}-90\lambda\)
\(-6\)	\(-3\)	\(\frac{ 1}{ 4}\)	\(-.12500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-.872284041I\)

\(\frac{ 9}{ 8}-\frac{ 872284041}{ 1000000000}I\)	\(\frac{ 3}{ 4}\)	\(\frac{ 1}{ 2}\)	\(1\)
\(-\frac{ 1}{ 4}\)	\(0\)	\(-1\)	\(0\)
\(3\)	\(-6\)	\(0\)	\(0\)
\(6\)	\(0\)	\(0\)	\(0\)

\(\frac{ 1}{ 16}+342\lambda\)	\(\frac{ 45}{ 32}+171\lambda\)	\(.27343750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-.483390739I\)	\(-.36685353e-1\)
\(\frac{ 7}{ 8}\)	\(\frac{ 23}{ 16}\)	\(-\frac{ 49}{ 192}\)	\(.27343750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+.483390739I\)
\(-\frac{ 3}{ 2}\)	\(\frac{ 9}{ 4}\)	\(\frac{ 23}{ 16}\)	\(\frac{ 45}{ 32}-171\lambda\)
\(-3\)	\(-\frac{ 3}{ 2}\)	\(\frac{ 7}{ 8}\)	\(\frac{ 1}{ 16}-342\lambda\)

\(\frac{ 15}{ 16}-342\lambda\)	\(\frac{ 9}{ 8}\)	\(\frac{ 1}{ 2}\)	\(1\)
\(-\frac{ 7}{ 8}\)	\(0\)	\(-1\)	\(0\)
\(\frac{ 3}{ 2}\)	\(-3\)	\(0\)	\(0\)
\(3\)	\(0\)	\(0\)	\(0\)

	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	,...

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

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

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

Explicit solution

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

Note:

Explicit solution

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:

Explicit solution

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:

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:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

Discriminant

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