Summary

You searched for: inst=289056/13

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New Number: 8.18 |  AESZ: 197  |  Superseeker: 3 1621/13  |  Hash: 4cc8bdba73e5fa6cb4089fa5296429de  

Degree: 8

\(13^{2} \theta^4-13^{2} x\left(41\theta^4+82\theta^3+67\theta^2+26\theta+4\right)-2^{3} 13 x^{2}\left(471\theta^4+1788\theta^3+2555\theta^2+1534\theta+338\right)+2^{6} 13 x^{3}\left(251\theta^4+1014\theta^3+1798\theta^2+1413\theta+405\right)+2^{9} x^{4}\left(749\theta^4+436\theta^3-4908\theta^2-6266\theta-2145\right)-2^{12} x^{5}\left(379\theta^4+1270\theta^3+967\theta^2-42\theta-178\right)-2^{15} x^{6}\left(9\theta^4-156\theta^3-273\theta^2-156\theta-28\right)+2^{18} x^{7}\left(13\theta^4+26\theta^3+20\theta^2+7\theta+1\right)-2^{21} x^{8}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 4, 68, 1552, 43156, ...
--> OEIS
Normalized instanton numbers (n0=1): 3, 226/13, 1621/13, 20666/13, 289056/13, ... ; Common denominator:...

Discriminant

\(-(z-1)(8z+1)(64z^2-48z+1)(-13+64z^2)^2\)

Local exponents

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

Note:

The operator has a second MUM-point at infinity, corresponding to operator 8.19.

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