Calabi-Yau differential operator database v.3.0

Summary

You searched for: sol=6673257595142837863377354000

Your search produced exactly one match

New Number: 2.46 | AESZ: | Superseeker: -2710944 -302270555492914464 | Hash: a06fc8c91c1e4c766fdb1e79370bef7a

Degree: 2

$\theta^4-2^{4} 3^{2} x\left(165888\theta^4+331776\theta^3+386496\theta^2+220608\theta+47711\right)+2^{22} 3^{10} x^{2}(4\theta+3)(4\theta+5)(6\theta+5)(6\theta+7)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 6870384, 63135105483024, 634962415293388429056, 6673257595142837863377354000, ...
--> OEIS
Normalized instanton numbers (n₀=1): -2710944, -717640301160, -302270555492914464, -171507700573958028578832, -113303073680022744870130144224, ... ; Common denominator:...

Discriminant

$(11943936z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 11943936}$ $\infty$
$0$ $0$ $\frac{ 3}{ 4}$
$0$ $-\frac{ 1}{ 2}$ $\frac{ 5}{ 6}$
$0$ $1$ $\frac{ 7}{ 6}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 5}{ 4}$

\(0\)	\(\frac{ 1}{ 11943936}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 3}{ 4}\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 5}{ 6}\)
\(0\)	\(1\)	\(\frac{ 7}{ 6}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 5}{ 4}\)

Note:

Operator equivalent to $\hat{9}$

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

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

Calabi-Yau differential operator database v.3

Summary

Discriminant

Local exponents

Note:

Monodromy (with respect to Frobenius basis)

Basis of the Doran-Morgan lattice

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

\(\frac{ 47}{ 24}\)	\(-4.710333822I\)	\(-\frac{ 1633}{ 576}\)	\(0\)
\(0\)	\(-\frac{ 47}{ 24}\)	\(0\)	\(-\frac{ 1633}{ 576}\)
\(1\)	\(0\)	\(-\frac{ 47}{ 24}\)	\(4.710333822I\)
\(0\)	\(1\)	\(0\)	\(\frac{ 47}{ 24}\)