Summary

You searched for: inst=-5421

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New Number: 8.4 |  AESZ: 160  |  Superseeker: 6 -325  |  Hash: 8ce8667fe6e49ce6625fafe044b1641b  

Degree: 8

\(\theta^4-3 x(3\theta^2+3\theta+1)(7\theta^2+7\theta+2)+3^{2} x^{2}\left(171\theta^4+396\theta^3+555\theta^2+318\theta+64\right)-2^{3} 3^{4} x^{3}\left(21\theta^4-126\theta^3-386\theta^2-291\theta-76\right)+2^{4} 3^{5} x^{4}\left(147\theta^4+294\theta^3+102\theta^2-45\theta-14\right)+2^{6} 3^{7} x^{5}\left(21\theta^4+210\theta^3+118\theta^2-19\theta-24\right)+2^{6} 3^{8} x^{6}\left(171\theta^4+288\theta^3+393\theta^2+288\theta+76\right)+2^{9} 3^{10} x^{7}(3\theta^2+3\theta+1)(7\theta^2+7\theta+2)+2^{12} 3^{12} x^{8}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 6, 90, 1176, 3114, ...
--> OEIS
Normalized instanton numbers (n0=1): 6, 6, -325, -1977/2, -5421, ... ; Common denominator:...

Discriminant

\((27z^2+9z+1)(1728z^2-72z+1)(1+216z^2)^2\)

Local exponents

\(-\frac{ 1}{ 6}-\frac{ 1}{ 18}\sqrt{ 3}I\)\(-\frac{ 1}{ 6}+\frac{ 1}{ 18}\sqrt{ 3}I\)\(0-\frac{ 1}{ 36}\sqrt{ 6}I\)\(0\)\(0+\frac{ 1}{ 36}\sqrt{ 6}I\)\(\frac{ 1}{ 48}-\frac{ 1}{ 144}\sqrt{ 3}I\)\(\frac{ 1}{ 48}+\frac{ 1}{ 144}\sqrt{ 3}I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(3\)\(1\)\(1\)\(1\)
\(2\)\(2\)\(4\)\(0\)\(4\)\(2\)\(2\)\(1\)

Note:

Hadamard product $a \ast f$. 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$Q(\sqrt{6})$.

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