Summary

You searched for: h3=128

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1

New Number: 5.96 |  AESZ: 339  |  Superseeker: 12 28  |  Hash: 41593acc689cf76c174442db98218947  

Degree: 5

\(\theta^4-2^{2} x\left(10\theta^4+50\theta^3+39\theta^2+14\theta+2\right)+2^{4} x^{2}\left(177\theta^4+1158\theta^3+2007\theta^2+1158\theta+230\right)+2^{8} x^{3}\left(539\theta^4+1344\theta^3-300\theta^2-1068\theta-340\right)+2^{10} 5 x^{4}(2\theta+1)(4\theta^3-642\theta^2-1002\theta-385)-2^{13} 3 5^{2} x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, 8, 0, -6400, -249200, ...
--> OEIS
Normalized instanton numbers (n0=1): 12, -339/2, 28, 27639/2, 634692, ... ; Common denominator:...

Discriminant

\(-(55296z^3-5632z^2+80z-1)(1+20z)^2\)

Local exponents

\(-\frac{ 1}{ 20}\)\(0\) ≈\(0.007072-0.012497I\) ≈\(0.007072+0.012497I\) ≈\(0.087707\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 2}{ 3}\)
\(3\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 4}{ 3}\)
\(4\)\(0\)\(2\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.96" from ...

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2

New Number: 5.9 |  AESZ: 56  |  Superseeker: -16 -3280  |  Hash: 58a7f24bf18cb98b526885069667f9f0  

Degree: 5

\(\theta^4-2^{4} x\left(22\theta^4+8\theta^3+9\theta^2+5\theta+1\right)+2^{9} x^{2}\left(94\theta^4+88\theta^3+97\theta^2+45\theta+8\right)-2^{14} x^{3}\left(194\theta^4+336\theta^3+371\theta^2+195\theta+41\right)+2^{19} 3 x^{4}\left(64\theta^4+176\theta^3+217\theta^2+129\theta+30\right)-2^{27} 3^{2} x^{5}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 16, 464, 17152, 725776, ...
--> OEIS
Normalized instanton numbers (n0=1): -16, -178, -3280, -76197, -2046896, ... ; Common denominator:...

Discriminant

\(-(-1+32z)(96z-1)^2(64z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 96}\)\(\frac{ 1}{ 64}\)\(\frac{ 1}{ 32}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)
\(0\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)
\(0\)\(4\)\(1\)\(2\)\(1\)

Note:

There is a second MUM-point hiding at infinity, corresponding to Operator...

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