Summary

You searched for: c3=-84

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1

New Number: 5.20 |  AESZ: 186  |  Superseeker: 49/19 1761/19  |  Hash: b3d164f22d02de1efcd62d3aa9ab5ce4  

Degree: 5

\(19^{2} \theta^4-19 x\left(700\theta^4+1238\theta^3+999\theta^2+380\theta+57\right)-x^{2}\left(64745\theta^4+368006\theta^3+609133\theta^2+412756\theta+102258\right)+3^{3} x^{3}\left(6397\theta^4+12198\theta^3-11923\theta^2-27360\theta-11286\right)+3^{6} x^{4}\left(64\theta^4+1154\theta^3+2425\theta^2+1848\theta+486\right)-3^{11} x^{5}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 3, 51, 1029, 25299, ...
--> OEIS
Normalized instanton numbers (n0=1): 49/19, 252/19, 1761/19, 18990/19, 246159/19, ... ; Common denominator:...

Discriminant

\(-(z+1)(243z^2+35z-1)(-19+27z)^2\)

Local exponents

\(-1\)\(-\frac{ 35}{ 486}-\frac{ 13}{ 486}\sqrt{ 13}\)\(0\)\(-\frac{ 35}{ 486}+\frac{ 13}{ 486}\sqrt{ 13}\)\(\frac{ 19}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding to Operator AESZ 187/5.21

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2

New Number: 8.26 |  AESZ: 301  |  Superseeker: 193/11 48570/11  |  Hash: a91db18876a9dfbf42b88f8d64c55d85  

Degree: 8

\(11^{2} \theta^4-11 x\left(1517\theta^4+3136\theta^3+2393\theta^2+825\theta+110\right)-x^{2}\left(24266+106953\theta+202166\theta^2+207620\theta^3+90362\theta^4\right)-x^{3}\left(53130+217437\theta+415082\theta^2+507996\theta^3+245714\theta^4\right)-x^{4}\left(15226+183269\theta+564786\theta^2+785972\theta^3+407863\theta^4\right)-x^{5}\left(25160+279826\theta+728323\theta^2+790148\theta^3+434831\theta^4\right)-2^{3} x^{6}\left(36361\theta^4+70281\theta^3+73343\theta^2+37947\theta+7644\right)-2^{4} 5 x^{7}\left(1307\theta^4+3430\theta^3+3877\theta^2+2162\theta+488\right)-2^{9} 5^{2} x^{8}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 10, 466, 32392, 2727826, ...
--> OEIS
Normalized instanton numbers (n0=1): 193/11, 1973/11, 48570/11, 1689283/11, 72444183/11, ... ; Common denominator:...

Discriminant

\(-(-1+143z+32z^2)(z+1)^2(20z^2+17z+11)^2\)

Local exponents

\(-\frac{ 143}{ 64}-\frac{ 19}{ 64}\sqrt{ 57}\)\(-1\)\(-\frac{ 17}{ 40}-\frac{ 1}{ 40}\sqrt{ 591}I\)\(-\frac{ 17}{ 40}+\frac{ 1}{ 40}\sqrt{ 591}I\)\(0\)\(-\frac{ 143}{ 64}+\frac{ 19}{ 64}\sqrt{ 57}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(1\)\(\frac{ 1}{ 2}\)\(3\)\(3\)\(0\)\(1\)\(1\)
\(2\)\(1\)\(4\)\(4\)\(0\)\(2\)\(1\)

Note:

This operator has a second MUM-point at infinity corresponding to operator 8.27.

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