Calabi-Yau differential operator database v.3.0

1

New Number: 4.19 | AESZ: ~66 | Superseeker: -864 -147560800 | Hash: b9b85f803521c6af3b5f7572d309f89a

Degree: 4

$\theta^4-2^{2} 3 x\left(1440\theta^4+2880\theta^3+3434\theta^2+1994\theta+447\right)+2^{4} 3^{4} x^{2}\left(76032\theta^4+304128\theta^3+518496\theta^2+428736\theta+143785\right)-2^{15} 3^{8} x^{3}(240\theta^2+720\theta+709)(2\theta+3)^2+2^{26} 3^{10} x^{4}(2\theta+3)(2\theta+5)(3\theta+5)(3\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 5364, 29367900, 170217457200, 1029027458497500, ...
--> OEIS
Normalized instanton numbers (n₀=1): -864, -261684, -147560800, -120568926924, -88009904955744, ... ; Common denominator:...

Discriminant

$(6912z-1)^2(1728z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 6912}$ $\frac{ 1}{ 1728}$ $\infty$
$0$ $0$ $0$ $\frac{ 3}{ 2}$
$0$ $-\frac{ 1}{ 2}$ $-\frac{ 1}{ 2}$ $\frac{ 5}{ 3}$
$0$ $1$ $1$ $\frac{ 7}{ 3}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 5}{ 2}$

\(0\)	\(\frac{ 1}{ 6912}\)	\(\frac{ 1}{ 1728}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 3}{ 2}\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 5}{ 3}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 7}{ 3}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to $AESZ 66 =$D \ast \alpha \tilde c \ast j$

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

2

New Number: 4.20 | AESZ: | Superseeker: -2484 -1327731388 | Hash: 80035e90a6f24cd6da3d4c5adc98379f

Degree: 4

$\theta^4-2^{2} 3 x\left(2448\theta^4+4896\theta^3+5773\theta^2+3325\theta+732\right)+2^{6} 3^{4} x^{2}\left(41688\theta^4+166752\theta^3+248973\theta^2+164442\theta+40616\right)-2^{8} 3^{8} x^{3}(816\theta^2+2448\theta+2389)(2\theta+3)^2+2^{14} 3^{10} x^{4}(2\theta+3)(2\theta+5)(3\theta+5)(3\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 8784, 99982728, 1239742123200, 16039070549564328, ...
--> OEIS
Normalized instanton numbers (n₀=1): -2484, -1446309, -1327731388, -1580284433106, -2187358898922144, ... ; Common denominator:...

Discriminant

$(1-14688z+186624z^2)^2$

Local exponents

$0$ $s_1$ $s_2$ $\frac{ 17}{ 432}-\frac{ 1}{ 36}\sqrt{ 2}$ $\frac{ 17}{ 432}+\frac{ 1}{ 36}\sqrt{ 2}$ $\infty$
$0$ $-\frac{ 1}{ 2}$ $-\frac{ 1}{ 2}$ $0$ $0$ $\frac{ 3}{ 2}$
$0$ $0$ $0$ $-\frac{ 1}{ 2}$ $-\frac{ 1}{ 2}$ $\frac{ 5}{ 3}$
$0$ $1$ $1$ $1$ $1$ $\frac{ 7}{ 3}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 5}{ 2}$

\(0\)	\(s_1\)	\(s_2\)	\(\frac{ 17}{ 432}-\frac{ 1}{ 36}\sqrt{ 2}\)	\(\frac{ 17}{ 432}+\frac{ 1}{ 36}\sqrt{ 2}\)	\(\infty\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(0\)	\(0\)	\(\frac{ 3}{ 2}\)
\(0\)	\(0\)	\(0\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 5}{ 3}\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(\frac{ 7}{ 3}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to AESZ 149=$D \ast \gamma ~tilde g \ast j$

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

3

New Number: 4.21 | AESZ: | Superseeker: -492 136094428 | Hash: 595707be6cb20abc1dfeecf72492ae5f

Degree: 4

$\theta^4-2^{2} 3 x\left(1008\theta^4+2016\theta^3+2411\theta^2+1403\theta+316\right)+2^{6} 3^{2} x^{2}\left(115992\theta^4+463968\theta^3+872325\theta^2+816714\theta+307516\right)-2^{8} 3^{12} x^{3}(336\theta^2+1008\theta+995)(2\theta+3)^2+2^{14} 3^{18} x^{4}(2\theta+3)(2\theta+5)(3\theta+5)(3\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 3792, 9275400, 7430606400, -68166524583000, ...
--> OEIS
Normalized instanton numbers (n₀=1): -492, 128514, 136094428, 32416215738, -16919954920032, ... ; Common denominator:...

Discriminant

$(15116544z^2-6048z+1)^2$

Local exponents

$0$ $s_1$ $s_2$ $\frac{ 7}{ 34992}-\frac{ 1}{ 8748}\sqrt{ 2}I$ $\frac{ 7}{ 34992}+\frac{ 1}{ 8748}\sqrt{ 2}I$ $\infty$
$0$ $-\frac{ 1}{ 2}$ $-\frac{ 1}{ 2}$ $0$ $0$ $\frac{ 3}{ 2}$
$0$ $0$ $0$ $-\frac{ 1}{ 2}$ $-\frac{ 1}{ 2}$ $\frac{ 5}{ 3}$
$0$ $1$ $1$ $1$ $1$ $\frac{ 7}{ 3}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 5}{ 2}$

\(0\)	\(s_1\)	\(s_2\)	\(\frac{ 7}{ 34992}-\frac{ 1}{ 8748}\sqrt{ 2}I\)	\(\frac{ 7}{ 34992}+\frac{ 1}{ 8748}\sqrt{ 2}I\)	\(\infty\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(0\)	\(0\)	\(\frac{ 3}{ 2}\)
\(0\)	\(0\)	\(0\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 5}{ 3}\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(\frac{ 7}{ 3}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 5}{ 2}\)

Note:

This is operator "4.21" from ...

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

4

New Number: 4.22 | AESZ: | Superseeker: -1488 -517984144 | Hash: 7d70f749f0fd6381c088f4c1fac4d6df

Degree: 4

$\theta^4-2^{4} 3 x\left(432\theta^4+864\theta^3+1023\theta^2+591\theta+131\right)+2^{9} 3^{2} x^{2}\left(24624\theta^4+98496\theta^3+151722\theta^2+106452\theta+29023\right)-2^{14} 3^{10} x^{3}(16\theta^2+48\theta+47)(2\theta+3)^2+2^{22} 3^{10} x^{4}(2\theta+3)(2\theta+5)(3\theta+5)(3\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 6288, 49006800, 416705452800, 3698851729136400, ...
--> OEIS
Normalized instanton numbers (n₀=1): -1488, -704730, -517984144, -469396561641, -493072108113648, ... ; Common denominator:...

Discriminant

$(2985984z^2-10368z+1)^2$

Local exponents

$0$ $s_1$ $s_2$ $\frac{ 1}{ 576}-\frac{ 1}{ 864}\sqrt{ 2}$ $\frac{ 1}{ 576}+\frac{ 1}{ 864}\sqrt{ 2}$ $\infty$
$0$ $-\frac{ 1}{ 2}$ $-\frac{ 1}{ 2}$ $0$ $0$ $\frac{ 3}{ 2}$
$0$ $0$ $0$ $-\frac{ 1}{ 2}$ $-\frac{ 1}{ 2}$ $\frac{ 5}{ 3}$
$0$ $1$ $1$ $1$ $1$ $\frac{ 7}{ 3}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 5}{ 2}$

\(0\)	\(s_1\)	\(s_2\)	\(\frac{ 1}{ 576}-\frac{ 1}{ 864}\sqrt{ 2}\)	\(\frac{ 1}{ 576}+\frac{ 1}{ 864}\sqrt{ 2}\)	\(\infty\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(0\)	\(0\)	\(\frac{ 3}{ 2}\)
\(0\)	\(0\)	\(0\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 5}{ 3}\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(\frac{ 7}{ 3}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to $D \ast \epsilon \tilde d \ast j$

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

5

New Number: 4.23 | AESZ: | Superseeker: -1116 -349462868 | Hash: 4cde44ecce8658b2c2ca6b3c279f4e62

Degree: 4

$\theta^4-2^{2} 3^{2} x\left(432\theta^4+864\theta^3+1023\theta^2+591\theta+131\right)+2^{4} 3^{5} 5 x^{2}\left(2592\theta^4+10368\theta^3+13788\theta^2+6840\theta+689\right)+2^{8} 3^{14} x^{3}(16\theta^2+48\theta+47)(2\theta+3)^2+2^{14} 3^{16} x^{4}(2\theta+3)(2\theta+5)(3\theta+5)(3\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 4716, 31430916, 223425214992, 1654537886846532, ...
--> OEIS
Normalized instanton numbers (n₀=1): -1116, -586989, -349462868, -300569202144, -280354383814176, ... ; Common denominator:...

Discriminant

$(5038848z^2+7776z-1)^2$

Local exponents

$-\frac{ 1}{ 1296}-\frac{ 1}{ 1944}\sqrt{ 3}$ $0$ $s_1$ $s_2$ $-\frac{ 1}{ 1296}+\frac{ 1}{ 1944}\sqrt{ 3}$ $\infty$
$0$ $0$ $-\frac{ 1}{ 2}$ $-\frac{ 1}{ 2}$ $0$ $\frac{ 3}{ 2}$
$-\frac{ 1}{ 2}$ $0$ $0$ $0$ $-\frac{ 1}{ 2}$ $\frac{ 5}{ 3}$
$1$ $0$ $1$ $1$ $1$ $\frac{ 7}{ 3}$
$\frac{ 3}{ 2}$ $0$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 5}{ 2}$

\(-\frac{ 1}{ 1296}-\frac{ 1}{ 1944}\sqrt{ 3}\)	\(0\)	\(s_1\)	\(s_2\)	\(-\frac{ 1}{ 1296}+\frac{ 1}{ 1944}\sqrt{ 3}\)	\(\infty\)
\(0\)	\(0\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(0\)	\(\frac{ 3}{ 2}\)
\(-\frac{ 1}{ 2}\)	\(0\)	\(0\)	\(0\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 5}{ 3}\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 7}{ 3}\)
\(\frac{ 3}{ 2}\)	\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 5}{ 2}\)

Note:

This is operator "4.23" from ...

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

6

New Number: 4.24 | AESZ: | Superseeker: -612 51318900 | Hash: dc90e303db3462d0c0bd472762000ad5

Degree: 4

$\theta^4-2^{2} 3 x\left(1584\theta^4+3168\theta^3+3799\theta^2+2215\theta+501\right)+2^{4} 3^{2} x^{2}\left(951264\theta^4+3805056\theta^3+6812388\theta^2+6014664\theta+2151443\right)-2^{8} 3^{8} 5^{3} x^{3}(528\theta^2+1584\theta+1567)(2\theta+3)^2+2^{14} 3^{10} 5^{6} x^{4}(2\theta+3)(2\theta+5)(3\theta+5)(3\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 6012, 31439916, 155468925360, 741919701370860, ...
--> OEIS
Normalized instanton numbers (n₀=1): -612, -87372, 51318900, 24336059400, 14111081636400, ... ; Common denominator:...

Discriminant

$(23328000z^2-9504z+1)^2$

Local exponents

$0$ $s_1$ $s_2$ $\frac{ 11}{ 54000}-\frac{ 1}{ 27000}I$ $\frac{ 11}{ 54000}+\frac{ 1}{ 27000}I$ $\infty$
$0$ $-\frac{ 1}{ 2}$ $-\frac{ 1}{ 2}$ $0$ $0$ $\frac{ 3}{ 2}$
$0$ $0$ $0$ $-\frac{ 1}{ 2}$ $-\frac{ 1}{ 2}$ $\frac{ 5}{ 3}$
$0$ $1$ $1$ $1$ $1$ $\frac{ 7}{ 3}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 5}{ 2}$

\(0\)	\(s_1\)	\(s_2\)	\(\frac{ 11}{ 54000}-\frac{ 1}{ 27000}I\)	\(\frac{ 11}{ 54000}+\frac{ 1}{ 27000}I\)	\(\infty\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(0\)	\(0\)	\(\frac{ 3}{ 2}\)
\(0\)	\(0\)	\(0\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 5}{ 3}\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(\frac{ 7}{ 3}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to $D \ast \eta ~b \ast j$

Calabi-Yau differential operator database v.3

Summary

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:

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:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice