Calabi-Yau differential operator database v.3.0

Summary

You searched for: sol=127808119824

Your search produced exactly one match

New Number: 2.48 | AESZ: ~94 | Superseeker: -1344 -109320512 | Hash: 892e497a83d12667b7f189a3d743fb7c

Degree: 2

$\theta^4-2^{2} 3 x\left(1152\theta^4+2304\theta^3+2710\theta^2+1558\theta+341\right)+2^{4} 3^{2} x^{2}(24\theta+19)(24\theta+23)(24\theta+25)(24\theta+29)$

Maple LaTex

Coefficients of the holomorphic solution: 1, 4092, 21900060, 127808119824, 778493560064220, ...
--> OEIS
Normalized instanton numbers (n₀=1): -1344, -278040, -109320512, -56290146024, -33748229589312, ... ; Common denominator:...

Discriminant

$(6912z-1)^2$

Local exponents

$0$ $\frac{ 1}{ 6912}$ $\infty$
$0$ $0$ $\frac{ 19}{ 24}$
$0$ $-\frac{ 1}{ 2}$ $\frac{ 23}{ 24}$
$0$ $1$ $\frac{ 25}{ 24}$
$0$ $\frac{ 3}{ 2}$ $\frac{ 29}{ 24}$

\(0\)	\(\frac{ 1}{ 6912}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 19}{ 24}\)
\(0\)	\(-\frac{ 1}{ 2}\)	\(\frac{ 23}{ 24}\)
\(0\)	\(1\)	\(\frac{ 25}{ 24}\)
\(0\)	\(\frac{ 3}{ 2}\)	\(\frac{ 29}{ 24}\)

Note:

Operator equivalent to $\hat{11}$

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

\(.918558654\)	\(-.664735808I\)	\(.63788795e-1\)	\(0\)
\(0\)	\(-\frac{ 3}{ 8}\sqrt{ 2}\sqrt{ 3}\)	\(0\)	\(.63788795e-1\)
\(\sqrt{ 6}\)	\(0\)	\(-\frac{ 3}{ 8}\sqrt{ 2}\sqrt{ 3}\)	\(.664735808I\)
\(0\)	\(\sqrt{ 6}\)	\(0\)	\(.918558654\)

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

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