Summary

You searched for: inst=500282

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New Number: 8.12 |  AESZ: 175  |  Superseeker: 17 1387  |  Hash: f6db11b5e593983f455489d5bb1003c5  

Degree: 8

\(\theta^4-x(10\theta^2+10\theta+3)(17\theta^2+17\theta+6)+3^{4} x^{2}\left(89\theta^4+452\theta^3+633\theta^2+362\theta+80\right)+2^{3} 3^{4} x^{3}\left(170\theta^4-1020\theta^3-3119\theta^2-2373\theta-648\right)-2^{4} 3^{8} x^{4}\left(97\theta^4+194\theta^3-238\theta^2-335\theta-114\right)+2^{6} 3^{8} x^{5}\left(170\theta^4+1700\theta^3+961\theta^2-125\theta-204\right)+2^{6} 3^{12} x^{6}\left(89\theta^4-96\theta^3-189\theta^2-96\theta-12\right)-2^{9} 3^{12} x^{7}(10\theta^2+10\theta+3)(17\theta^2+17\theta+6)+2^{12} 3^{16} x^{8}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 18, 630, 29016, 1529766, ...
--> OEIS
Normalized instanton numbers (n0=1): 17, -299/4, 1387, -47623/2, 500282, ... ; Common denominator:...

Discriminant

\((81z-1)(8z-1)(72z-1)(9z-1)(-1+648z^2)^2\)

Local exponents

\(-\frac{ 1}{ 36}\sqrt{ 2}\)\(0\)\(\frac{ 1}{ 81}\)\(\frac{ 1}{ 72}\)\(\frac{ 1}{ 36}\sqrt{ 2}\)\(\frac{ 1}{ 9}\)\(\frac{ 1}{ 8}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(3\)\(0\)\(1\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(4\)\(0\)\(2\)\(2\)\(4\)\(2\)\(2\)\(1\)

Note:

Hadamard product $c \ast g$. This operator has a second MUM-point
at infinity with the same instanton numbers. It can be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\sqrt{?})$.

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