Summary

You searched for: inst=7584

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New Number: 8.19 |  AESZ: 201  |  Superseeker: 32 7584  |  Hash: d21570c07bca6887061716b2d727fa75  

Degree: 8

\(\theta^4-2^{4} x\left(13\theta^4+26\theta^3+20\theta^2+7\theta+1\right)+2^{8} x^{2}\left(9\theta^4+192\theta^3+249\theta^2+114\theta+20\right)+2^{12} x^{3}\left(379\theta^4+246\theta^3-569\theta^2-318\theta-60\right)-2^{16} x^{4}\left(749\theta^4+2560\theta^3-1722\theta^2-1862\theta-474\right)-2^{20} 13 x^{5}\left(251\theta^4-10\theta^3+262\theta^2+145\theta+27\right)+2^{24} 13 x^{6}\left(471\theta^4+96\theta^3+17\theta^2+96\theta+42\right)+2^{28} 13^{2} x^{7}\left(41\theta^4+82\theta^3+67\theta^2+26\theta+4\right)-2^{35} 13^{2} x^{8}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 16, 752, 49408, 3805456, ...
--> OEIS
Normalized instanton numbers (n0=1): 32, -152, 7584, -160593, 7055200, ... ; Common denominator:...

Discriminant

\(-(128z-1)(16z+1)(256z^2-96z+1)(-1+3328z^2)^2\)

Local exponents

\(-\frac{ 1}{ 16}\)\(-\frac{ 1}{ 208}\sqrt{ 13}\)\(0\)\(\frac{ 1}{ 128}\)\(\frac{ 3}{ 16}-\frac{ 1}{ 8}\sqrt{ 2}\)\(\frac{ 1}{ 208}\sqrt{ 13}\)\(\frac{ 3}{ 16}+\frac{ 1}{ 8}\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(1\)\(3\)\(1\)\(1\)
\(2\)\(4\)\(0\)\(2\)\(2\)\(4\)\(2\)\(1\)

Note:

This operator has a second MUM-point, corresponding to operator 8.18

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