Calabi-Yau differential operator database v.3.0

Summary

Your search produced exactly one match

New Number: 2.67 | AESZ: 245 | Superseeker: -6 -170 | Hash: 0ef0bca0dbecbedad92696fd7c0f9e42

Degree: 2

\(\theta^4-2 3 x\left(36\theta^4+66\theta^3+61\theta^2+28\theta+5\right)+2^{2} 3^{2} x^{2}(3\theta+2)^2(6\theta+7)^2\)

Coefficients of the holomorphic solution: 1, 30, 1764, 127776, 10248750, ...
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Normalized instanton numbers (n₀=1): -6, -33, -170, -1029, -3246, ... ; Common denominator:...

Discriminant

\((108z-1)^2\)

Local exponents

\(0\) \(\frac{ 1}{ 108}\) \(\infty\)
\(0\) \(0\) \(\frac{ 2}{ 3}\)
\(0\) \(\frac{ 1}{ 6}\) \(\frac{ 2}{ 3}\)
\(0\) \(1\) \(\frac{ 7}{ 6}\)
\(0\) \(\frac{ 7}{ 6}\) \(\frac{ 7}{ 6}\)

\(0\)	\(\frac{ 1}{ 108}\)	\(\infty\)
\(0\)	\(0\)	\(\frac{ 2}{ 3}\)
\(0\)	\(\frac{ 1}{ 6}\)	\(\frac{ 2}{ 3}\)
\(0\)	\(1\)	\(\frac{ 7}{ 6}\)
\(0\)	\(\frac{ 7}{ 6}\)	\(\frac{ 7}{ 6}\)

Note:

This is operator "2.67" from ...

Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, -6, -270, -4596, -66126, -405756, 8587836, 424349304,...
Coefficients of the q-coordinate : 0, 1, -48, 1440, -32848, 637872, -11009952, 174295160,...

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

No topological data

Monodromy (with respect to Frobenius basis)

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

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\(1.052168056+.90357723e-1I\)	\(\frac{ 1}{ 4}-\frac{ 1}{ 12}I\sqrt{ 3}\)	\(-33^{ \frac{ 1}{ 6}}Pi^{ \frac{ 9}{ 2}}Zeta(5)^6-6\lambda\)	\(.10688274e-1-\frac{ 1}{ 5}I5^{ \frac{ 4}{ 7}}ln(2)^12\)
\(\frac{ 3}{ 2}-\frac{ 1}{ 2}I\sqrt{ 3}\)	\(\frac{ 3}{ 4}-\frac{ 1}{ 4}I\sqrt{ 3}\)	\(-\frac{ 1}{ 8}+\frac{ 1}{ 24}I\sqrt{ 3}\)	\(33^{ \frac{ 1}{ 6}}Pi^{ \frac{ 9}{ 2}}Zeta(5)^6+6\lambda\)
\(0\)	\(\frac{ 9}{ 2}-\frac{ 3}{ 2}I\sqrt{ 3}\)	\(\frac{ 3}{ 4}-\frac{ 1}{ 4}I\sqrt{ 3}\)	\(\frac{ 1}{ 4}-\frac{ 1}{ 12}I\sqrt{ 3}\)
\(-27+9I\sqrt{ 3}\)	\(0\)	\(\frac{ 3}{ 2}-\frac{ 1}{ 2}I\sqrt{ 3}\)	\(.447831944-.956383127I\)

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Basis of the Doran-Morgan lattice

\(-\frac{ 6521007}{ 125000000}-\frac{ 90357723}{ 1000000000}I\)	\(-3+\frac{ 4511615154067544842086723740124334848694351954431101272196462779644508392806538050844596873167533211}{ 2604782223680891931509451724762066519358428478691519147090699072692122550847025398588836869330367971}I\)	\(\frac{ 1}{ 2}-\frac{ 3081490456277555159153769728602633601692409347626414678367139999430219011336903561652776870289659281}{ 3558198688874218386798087732443200684026390216561310209643580926168315471826781724716716871248950591}I\)	\(1\)
\(-\frac{ 3}{ 2}+\frac{ 1}{ 2}I\sqrt{ 3}\)	\(\frac{ 27}{ 2}-\frac{ 5941739851857534525019677751646036095696294561235787866025785559858797774276172540036416876045407141}{ 762325578427705482137746574067229488156369299800529597635468373844463859062368874404292289563613477}I\)	\(-\frac{ 1}{ 2}+\frac{ 3081490456277555159153769728602633601692409347626414678367139999430219011336903561652776870289659281}{ 3558198688874218386798087732443200684026390216561310209643580926168315471826781724716716871248950591}I\)	\(0\)
\(0\)	\(-27+\frac{ 11883479703715069050039355503292072191392589122471575732051571119717595548552345080072833752090814282}{ 762325578427705482137746574067229488156369299800529597635468373844463859062368874404292289563613477}I\)	\(0\)	\(0\)
\(27-\frac{ 11883479703715069050039355503292072191392589122471575732051571119717595548552345080072833752090814282}{ 762325578427705482137746574067229488156369299800529597635468373844463859062368874404292289563613477}I\)	\(0\)	\(0\)	\(0\)

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