Calabi-Yau differential operator database v.3.0

1

New Number: 4.10 | AESZ: | Superseeker: -84 -148820 | Hash: fc2837f1001e57a5cc53749a08d4f2bf

Degree: 4

$\theta^4-2 3 x\left(216\theta^4+432\theta^3+516\theta^2+300\theta+67\right)+2^{2} 3^{2} x^{2}\left(12312\theta^4+49248\theta^3+76374\theta^2+54252\theta+15017\right)-2^{6} 3^{10} x^{3}(\theta^2+3\theta+3)(2\theta+3)^2+2^{4} 3^{10} x^{4}(2\theta+3)(2\theta+5)(6\theta+11)(6\theta+13)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 402, 197010, 104962956, 58311249066, ...
--> OEIS
Normalized instanton numbers (n₀=1): -84, -5271/2, -148820, -41373213/4, -836813460, ... ; Common denominator:...

Discriminant

$(1-648z+11664z^2)^2$

Local exponents

$0$ $s_1$ $s_2$ $\frac{ 1}{ 36}-\frac{ 1}{ 54}\sqrt{ 2}$ $\frac{ 1}{ 36}+\frac{ 1}{ 54}\sqrt{ 2}$ $\infty$
$0$ $-\frac{ 1}{ 2}$ $-\frac{ 1}{ 2}$ $0$ $0$ $\frac{ 3}{ 2}$
$0$ $0$ $0$ $-\frac{ 1}{ 2}$ $-\frac{ 1}{ 2}$ $\frac{ 11}{ 6}$
$0$ $1$ $1$ $1$ $1$ $\frac{ 13}{ 6}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 5}{ 2}$

\(0\)	\(s_1\)	\(s_2\)	\(\frac{ 1}{ 36}-\frac{ 1}{ 54}\sqrt{ 2}\)	\(\frac{ 1}{ 36}+\frac{ 1}{ 54}\sqrt{ 2}\)	\(\infty\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(0\)	\(0\)	\(\frac{ 3}{ 2}\)
\(0\)	\(0\)	\(0\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 11}{ 6}\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(\frac{ 13}{ 6}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to AESZ 170=$d \ast h \tilde B \ast \epsilon$

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

2

New Number: 4.11 | AESZ: | Superseeker: -63 -96866 | Hash: 39ed55f37672c58e7ce182c4c33d4a66

Degree: 4

$\theta^4-x\left(972\theta^4+1944\theta^3+2322\theta^2+1350\theta+603/2\right)+x^{2}\left(196830\theta^4+787320\theta^3+2110455/2\theta^2+535815\theta+237897/4\right)+3^{14} x^{3}(\theta^2+3\theta+3)(2\theta+3)^2+x^{4}43046721/16(2\theta+3)(2\theta+5)(6\theta+11)(6\theta+13)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 603/2, 1008855/8, 898513875/16, 3331190162475/128, ...
--> OEIS
Normalized instanton numbers (n₀=1): -63, -8757/4, -96866, -6253821, -446217723, ... ; Common denominator:...

Discriminant

$(-1+486z+19683z^2)^2$

Local exponents

$-\frac{ 1}{ 81}-\frac{ 2}{ 243}\sqrt{ 3}$ $0$ $s_1$ $s_2$ $-\frac{ 1}{ 81}+\frac{ 2}{ 243}\sqrt{ 3}$ $\infty$
$0$ $0$ $-\frac{ 1}{ 2}$ $-\frac{ 1}{ 2}$ $0$ $\frac{ 3}{ 2}$
$-\frac{ 1}{ 2}$ $0$ $0$ $0$ $-\frac{ 1}{ 2}$ $\frac{ 11}{ 6}$
$1$ $0$ $1$ $1$ $1$ $\frac{ 13}{ 6}$
$\frac{ 3}{ 2}$ $0$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 5}{ 2}$

\(-\frac{ 1}{ 81}-\frac{ 2}{ 243}\sqrt{ 3}\)	\(0\)	\(s_1\)	\(s_2\)	\(-\frac{ 1}{ 81}+\frac{ 2}{ 243}\sqrt{ 3}\)	\(\infty\)
\(0\)	\(0\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(0\)	\(\frac{ 3}{ 2}\)
\(-\frac{ 1}{ 2}\)	\(0\)	\(0\)	\(0\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 11}{ 6}\)
\(1\)	\(0\)	\(1\)	\(1\)	\(1\)	\(\frac{ 13}{ 6}\)
\(\frac{ 3}{ 2}\)	\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 5}{ 2}\)

Note:

This is operator "4.11" from ...

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

3

New Number: 4.12 | AESZ: | Superseeker: -45 7080 | Hash: 6c95cb50a57e8a1c96a5a4e3e353cb85

Degree: 4

$\theta^4-x\left(1188\theta^4+2376\theta^3+2874\theta^2+1686\theta+765/2\right)+x^{2}\left(535086\theta^4+2140344\theta^3+7708527/2\theta^2+3427839\theta+4938345/4\right)-3^{8} 5^{3} x^{3}(33\theta^2+99\theta+100)(2\theta+3)^2+x^{4}922640625/16(2\theta+3)(2\theta+5)(6\theta+11)(6\theta+13)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 765/2, 1009575/8, 627988725/16, 1505754528075/128, ...
--> OEIS
Normalized instanton numbers (n₀=1): -45, -135, 7080, 406035, 17168436, ... ; Common denominator:...

Discriminant

$(1-594z+91125z^2)^2$

Local exponents

$0$ $s_1$ $s_2$ $\frac{ 11}{ 3375}-\frac{ 2}{ 3375}I$ $\frac{ 11}{ 3375}+\frac{ 2}{ 3375}I$ $\infty$
$0$ $-\frac{ 1}{ 2}$ $-\frac{ 1}{ 2}$ $0$ $0$ $\frac{ 3}{ 2}$
$0$ $0$ $0$ $-\frac{ 1}{ 2}$ $-\frac{ 1}{ 2}$ $\frac{ 11}{ 6}$
$0$ $1$ $1$ $1$ $1$ $\frac{ 13}{ 6}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 5}{ 2}$

\(0\)	\(s_1\)	\(s_2\)	\(\frac{ 11}{ 3375}-\frac{ 2}{ 3375}I\)	\(\frac{ 11}{ 3375}+\frac{ 2}{ 3375}I\)	\(\infty\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(0\)	\(0\)	\(\frac{ 3}{ 2}\)
\(0\)	\(0\)	\(0\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 11}{ 6}\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(\frac{ 13}{ 6}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 5}{ 2}\)

Note:

YY-operator equivalent to AESZ $=b \ast h ~B \ast \eta$

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

4

New Number: 4.7 | AESZ: | Superseeker: -54 -40552 | Hash: ee8508b4e5567367ca11f74e074e8099

Degree: 4

$\theta^4-2 3 x\left(180\theta^4+360\theta^3+433\theta^2+253\theta+57\right)+2^{2} 3^{4} 11 x^{2}\left(108\theta^4+432\theta^3+741\theta^2+618\theta+209\right)-2^{5} 3^{8} x^{3}(60\theta^2+180\theta+181)(2\theta+3)^2+2^{8} 3^{10} x^{4}(2\theta+3)(2\theta+5)(6\theta+11)(6\theta+13)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 342, 117990, 42901884, 16240501782, ...
--> OEIS
Normalized instanton numbers (n₀=1): -54, -864, -40552, -2192400, -123334380, ... ; Common denominator:...

Discriminant

$(432z-1)^2(108z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 432}$ $\frac{ 1}{ 108}$ $\infty$
$0$ $0$ $0$ $\frac{ 3}{ 2}$
$0$ $-\frac{ 1}{ 2}$ $-\frac{ 1}{ 2}$ $\frac{ 11}{ 6}$
$0$ $1$ $1$ $\frac{ 13}{ 6}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 5}{ 2}$

\(0\)	\(\frac{ 1}{ 432}\)	\(\frac{ 1}{ 108}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(\frac{ 3}{ 2}\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 11}{ 6}\)
\(0\)	\(1\)	\(1\)	\(\frac{ 13}{ 6}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 5}{ 2}\)

Note:

YY-operator equivalent to (:AESZ 50), $\tilde B \ast \alpha$

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

5

New Number: 4.8 | AESZ: | Superseeker: -135 -417685 | Hash: f5702d0b3fd53e9b80a42c76a335b648

Degree: 4

$\theta^4-x\left(1836\theta^4+3672\theta^3+4368\theta^2+2532\theta+1125/2\right)+x^{2}\left(844182\theta^4+3376728\theta^3+10153755/2\theta^2+3400299\theta+3426705/4\right)-x^{3}6561/2(2\theta+3)^2(102\theta^2+306\theta+305)+x^{4}59049/16(2\theta+3)(2\theta+5)(6\theta+11)(6\theta+13)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 1125/2, 3219615/8, 5002535925/16, 32404173968475/128, ...
--> OEIS
Normalized instanton numbers (n₀=1): -135, -22815/4, -417685, -78983235/2, -4331084310, ... ; Common denominator:...

Discriminant

$(1-918z+729z^2)^2$

Local exponents

$0$ $s_1$ $s_2$ $\frac{ 17}{ 27}-\frac{ 4}{ 9}\sqrt{ 2}$ $\frac{ 17}{ 27}+\frac{ 4}{ 9}\sqrt{ 2}$ $\infty$
$0$ $-\frac{ 1}{ 2}$ $-\frac{ 1}{ 2}$ $0$ $0$ $\frac{ 3}{ 2}$
$0$ $0$ $0$ $-\frac{ 1}{ 2}$ $-\frac{ 1}{ 2}$ $\frac{ 11}{ 6}$
$0$ $1$ $1$ $1$ $1$ $\frac{ 13}{ 6}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 5}{ 2}$

\(0\)	\(s_1\)	\(s_2\)	\(\frac{ 17}{ 27}-\frac{ 4}{ 9}\sqrt{ 2}\)	\(\frac{ 17}{ 27}+\frac{ 4}{ 9}\sqrt{ 2}\)	\(\infty\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(0\)	\(0\)	\(\frac{ 3}{ 2}\)
\(0\)	\(0\)	\(0\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 11}{ 6}\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(\frac{ 13}{ 6}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to AESZ 53 =$B \ast \gamma \tilde g \ast h$

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

6

New Number: 4.9 | AESZ: | Superseeker: -33 29693 | Hash: c444fb1a912bd488ee5947b8bc1e2c53

Degree: 4

$\theta^4-x\left(756\theta^4+1512\theta^3+1824\theta^2+1068\theta+483/2\right)+x^{2}\left(260982\theta^4+1043928\theta^3+3947211/2\theta^2+1859355\theta+2817729/4\right)-x^{3}531441/2(2\theta+3)^2(42\theta^2+126\theta+127)+x^{4}387420489/16(2\theta+3)(2\theta+5)(6\theta+11)(6\theta+13)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 483/2, 300015/8, 32162403/16, -132658029189/128, ...
--> OEIS
Normalized instanton numbers (n₀=1): -33, 1095/2, 29693, 1241103/2, -16117818, ... ; Common denominator:...

Discriminant

$(1-378z+59049z^2)^2$

Local exponents

$0$ $s_1$ $s_2$ $\frac{ 7}{ 2187}-\frac{ 4}{ 2187}\sqrt{ 2}I$ $\frac{ 7}{ 2187}+\frac{ 4}{ 2187}\sqrt{ 2}I$ $\infty$
$0$ $-\frac{ 1}{ 2}$ $-\frac{ 1}{ 2}$ $0$ $0$ $\frac{ 3}{ 2}$
$0$ $0$ $0$ $-\frac{ 1}{ 2}$ $-\frac{ 1}{ 2}$ $\frac{ 11}{ 6}$
$0$ $1$ $1$ $1$ $1$ $\frac{ 13}{ 6}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 3}{ 2}$ $\frac{ 5}{ 2}$

\(0\)	\(s_1\)	\(s_2\)	\(\frac{ 7}{ 2187}-\frac{ 4}{ 2187}\sqrt{ 2}I\)	\(\frac{ 7}{ 2187}+\frac{ 4}{ 2187}\sqrt{ 2}I\)	\(\infty\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(0\)	\(0\)	\(\frac{ 3}{ 2}\)
\(0\)	\(0\)	\(0\)	\(-\frac{ 1}{ 2}\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 11}{ 6}\)
\(0\)	\(1\)	\(1\)	\(1\)	\(1\)	\(\frac{ 13}{ 6}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 3}{ 2}\)	\(\frac{ 5}{ 2}\)

Note:

YY-operator equivalent to AESZ 151=$B \ast \delta$

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