Calabi-Yau differential operator database v.3.0

Summary

You searched for: sol=49063316029156400400

Your search produced exactly one match

New Number: 2.49 | AESZ: | Superseeker: -26400 -230398034080 | Hash: ffdc338b55d1f4e1f989f4359b06df6c

Degree: 2

$\theta^4-2^{4} 3 x\left(4608\theta^4+9216\theta^3+10744\theta^2+6136\theta+1325\right)+2^{12} 3^{2} x^{2}(24\theta+17)(24\theta+23)(24\theta+25)(24\theta+31)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 63600, 5412963600, 504140776339200, 49063316029156400400, ...
--> OEIS
Normalized instanton numbers (n₀=1): -26400, -52511160, -230398034080, -1287524740195200, -8504689433002312800, ... ; Common denominator:...

Discriminant

$(110592z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 110592}$ $\infty$
$0$ $0$ $\frac{ 17}{ 24}$
$0$ $-\frac{ 1}{ 2}$ $\frac{ 23}{ 24}$
$0$ $1$ $\frac{ 25}{ 24}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 31}{ 24}$

\(0\)	\(\frac{ 1}{ 110592}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 17}{ 24}\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 23}{ 24}\)
\(0\)	\(1\)	\(\frac{ 25}{ 24}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 31}{ 24}\)

Note:

Operator equivalent to $\hat{12}$

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

\(1.001734607\)	\(-1.096529708I\)	\(-.2455232e-2\)	\(0\)
\(0\)	\(-1.001734607\)	\(0\)	\(-.2455232e-2\)
\(\sqrt{ 2}\)	\(0\)	\(-1.001734607\)	\(1.096529708I\)
\(0\)	\(\sqrt{ 2}\)	\(0\)	\(1.001734607\)

\(cy[DM_basis]\)	\(\)	\(\)	\(\)
\(\)	\(\)	\(\)	\(\)
\(\)	\(\)	\(\)	\(\)
\(\)	\(\)	\(\)	\(\)

Calabi-Yau differential operator database v.3

Summary

Discriminant

Local exponents

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

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