Summary

You searched for: Spectrum0=1/3,1/3,2/3,2/3

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1

New Number: 4.47 |  AESZ: 239  |  Superseeker: 1584 171534960  |  Hash: 8e610c3437d7f38e552038bc55399495  

Degree: 4

\(\theta^4+2^{4} 3 x\left(9\theta^4-198\theta^3-131\theta^2-32\theta-3\right)-2^{11} 3^{2} x^{2}\left(486\theta^4+1215\theta^3+81\theta^2-27\theta-5\right)-2^{16} 3^{5} x^{3}\left(891\theta^4+972\theta^3+675\theta^2+216\theta+25\right)-2^{23} 3^{8} x^{4}(3\theta+1)^2(3\theta+2)^2\)

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Coefficients of the holomorphic solution: 1, 144, 147600, 239904000, 479672701200, ...
--> OEIS
Normalized instanton numbers (n0=1): 1584, -17874, 171534960, 30012731550, 105934107802896, ... ; Common denominator:...

Discriminant

\(-(432z+1)(3456z-1)(1+1728z)^2\)

Local exponents

\(-\frac{ 1}{ 432}\)\(-\frac{ 1}{ 1728}\)\(0\)\(\frac{ 1}{ 3456}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(1\)\(1\)\(0\)\(1\)\(\frac{ 1}{ 3}\)
\(1\)\(3\)\(0\)\(1\)\(\frac{ 2}{ 3}\)
\(2\)\(4\)\(0\)\(2\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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2

New Number: 4.68 |  AESZ: 337  |  Superseeker: 2043/5 88982631/5  |  Hash: dc26e94a7c1daba6f627be36c42019b7  

Degree: 4

\(5^{2} \theta^4-3 5 x\left(3483\theta^4+6102\theta^3+4241\theta^2+1190\theta+120\right)+2^{5} 3^{2} x^{2}\left(31428\theta^4+35559\theta^3+243\theta^2-4320\theta-740\right)-2^{8} 3^{5} x^{3}\left(7371\theta^4+4860\theta^3+2997\theta^2+1080\theta+140\right)+2^{13} 3^{8} x^{4}(3\theta+1)^2(3\theta+2)^2\)

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Coefficients of the holomorphic solution: 1, 72, 41400, 37396800, 41397463800, ...
--> OEIS
Normalized instanton numbers (n0=1): 2043/5, 279018/5, 88982631/5, 8604708876, 25774859896713/5, ... ; Common denominator:...

Discriminant

\((23328z^2-1917z+1)(-5+432z)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 71}{ 1728}-\frac{ 17}{ 1728}\sqrt{ 17}\)\(\frac{ 5}{ 432}\)\(\frac{ 71}{ 1728}+\frac{ 17}{ 1728}\sqrt{ 17}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 3}\)
\(0\)\(1\)\(1\)\(1\)\(3\)\(1\)\(\frac{ 2}{ 3}\)
\(0\)\(2\)\(2\)\(2\)\(4\)\(2\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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