Calabi-Yau differential operator database v.3

New Number: 5.59 |  AESZ: 267  |  Superseeker: 1818 467810538  |  Hash: 924287a9ba8517571071ec73d860af7e  

Degree: 5

\(\theta^4+3^{2} x\left(729\theta^4-972\theta^3-684\theta^2-198\theta-31\right)+2 3^{8} x^{2}\left(567\theta^4-2592\theta^3+405\theta^2+189\theta+70\right)-2 3^{14} x^{3}\left(1377\theta^4+972\theta^3+1161\theta^2+459\theta+113\right)-3^{22} 5 x^{4}\left(27\theta^4-38\theta^2-38\theta-12\right)+3^{30} 5^{2} x^{5}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 279, 124011, 64869777, 36848978379, ...
--> OEIS
Normalized instanton numbers (n₀=1): 1818, -681336, 467810538, -422903176767, 446062311232740, ... ; Common denominator:...

Discriminant

\((1+729z)(3645z+1)^2(729z-1)^2\)

Local exponents

\(-\frac{ 1}{ 729}\)	\(-\frac{ 1}{ 3645}\)	\(0\)	\(\frac{ 1}{ 729}\)	\(\infty\)
\(0\)	\(0\)	\(0\)	\(0\)	\(1\)
\(1\)	\(1\)	\(0\)	\(0\)	\(1\)
\(1\)	\(3\)	\(0\)	\(1\)	\(1\)
\(2\)	\(4\)	\(0\)	\(1\)	\(1\)

Note:

There is a second MUM-point at infinity, corresponding to
Operator AESZ 266/5.58

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