Calabi-Yau differential operator database v.3.0

Summary

You searched for: sol=1581137831289447900

Your search produced exactly one match

New Number: 2.45 | AESZ: ~82 | Superseeker: -10080 -24400330080 | Hash: 11afa89027677e0616228cad62a9f990

Degree: 2

$\theta^4-2^{2} 3^{2} x\left(2592\theta^4+5184\theta^3+6066\theta^2+3474\theta+755\right)+2^{4} 3^{10} x^{2}(4\theta+3)(4\theta+5)(12\theta+11)(12\theta+13)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 27180, 978471900, 38487760088400, 1581137831289447900, ...
--> OEIS
Normalized instanton numbers (n₀=1): -10080, -11338740, -24400330080, -69157402598340, -228492096441648480, ... ; Common denominator:...

Discriminant

$(46656z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 46656}$ $\infty$
$0$ $0$ $\frac{ 3}{ 4}$
$0$ $-\frac{ 1}{ 2}$ $\frac{ 11}{ 12}$
$0$ $1$ $\frac{ 13}{ 12}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 5}{ 4}$

\(0\)	\(\frac{ 1}{ 46656}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 3}{ 4}\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 11}{ 12}\)
\(0\)	\(1\)	\(\frac{ 13}{ 12}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 5}{ 4}\)

Note:

Operator equivalent to $\hat{8}$

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

\(\frac{ 5}{ 8}\sqrt{ 3}\)	\(-1.175097994I\)	\(-.99232078e-1\)	\(0\)
\(0\)	\(-1.082531755\)	\(0\)	\(-.99232078e-1\)
\(\sqrt{ 3}\)	\(0\)	\(-1.082531755\)	\(1.175097994I\)
\(0\)	\(\sqrt{ 3}\)	\(0\)	\(\frac{ 5}{ 8}\sqrt{ 3}\)

\(cy[DM_basis]\)	\(\)	\(\)	\(\)
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Calabi-Yau differential operator database v.3

Summary

Discriminant

Local exponents

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

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