Summary

You searched for: sol=25872

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1

New Number: 12.9 |  AESZ:  |  Superseeker: 800 38825120  |  Hash: 7e2f8423069147eb36cfd1d714d1996a  

Degree: 12

\(\theta^4+2^{4} x\left(288\theta^4-96\theta^3-24\theta^2+24\theta+7\right)+2^{13} x^{2}\left(864\theta^4-240\theta^3+438\theta^2+96\theta-7\right)+2^{20} x^{3}\left(3856\theta^4+1152\theta^3+1036\theta^2+192\theta-53\right)+2^{30} x^{4}\left(636\theta^4-1440\theta^3-2303\theta^2-1988\theta-672\right)-2^{38} x^{5}\left(320\theta^4+7928\theta^3+14109\theta^2+11270\theta+3517\right)-2^{48} x^{6}\left(134\theta^4+1830\theta^3+3688\theta^2+3585\theta+1195\right)-2^{56} x^{7}\left(187\theta^4+356\theta^3-2355\theta^2-2866\theta-1199\right)-2^{65} x^{8}\left(91\theta^4+202\theta^3-1069\theta^2-2020\theta-948\right)-2^{74} x^{9}\left(2\theta^4-120\theta^3-211\theta^2-198\theta-69\right)+2^{84} x^{10}\left(\theta^4+44\theta^3+122\theta^2+121\theta+41\right)+2^{92} x^{11}(\theta^2+2\theta+2)(\theta+1)^2+2^{101} x^{12}(\theta+1)^2(\theta+2)^2\)

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Coefficients of the holomorphic solution: 1, -112, 25872, -5691136, 1522998544, ...
--> OEIS
Normalized instanton numbers (n0=1): 800, -121088, 38825120, -15641910336, 7303803435104, ... ; Common denominator:...

Discriminant

\((256z-1)(512z+1)(65536z^2-256z-1)(256z+1)^2(67108864z^3+1792z+1)^2\)

Local exponents

\(-\frac{ 1}{ 256}\)\(\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\)\(-\frac{ 1}{ 512}\) ≈\(-0.000552\)\(0\) ≈\(0.000276-0.00519I\) ≈\(0.000276+0.00519I\)\(\frac{ 1}{ 256}\)\(\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(\frac{ 1}{ 2}\)\(1\)\(1\)\(3\)\(0\)\(3\)\(3\)\(1\)\(1\)\(2\)
\(1\)\(2\)\(2\)\(4\)\(0\)\(4\)\(4\)\(2\)\(2\)\(2\)

Note:

This is operator "12.9" from ...

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2

New Number: 15.1 |  AESZ:  |  Superseeker: 800 38825120  |  Hash: c26e6797c51f4c09c1dfbc9e354ce168  

Degree: 15

\(\theta^4+2^{4} x\left(240\theta^4-96\theta^3-24\theta^2+24\theta+7\right)+2^{12} x^{2}\left(912\theta^4-192\theta^3+948\theta^2+120\theta-35\right)-2^{21} x^{3}\left(240\theta^4-1152\theta^3+832\theta^2+156\theta-5\right)-2^{29} x^{4}\left(2064\theta^4+5280\theta^3+4834\theta^2+3988\theta+1289\right)+2^{36} x^{5}\left(928\theta^4-10496\theta^3-26568\theta^2-20840\theta-6149\right)+2^{44} x^{6}\left(5472\theta^4+47424\theta^3+81628\theta^2+53832\theta+15073\right)-2^{54} x^{7}\left(736\theta^4+1808\theta^3-13652\theta^2-22662\theta-9257\right)+2^{62} x^{8}\left(228\theta^4-11376\theta^3-49855\theta^2-49982\theta-17627\right)+2^{72} x^{9}\left(111\theta^4+2454\theta^3+5183\theta^2+855\theta-620\right)-2^{80} x^{10}\left(319\theta^4+1592\theta^3-3479\theta^2-8814\theta-4317\right)+2^{89} x^{11}\left(63\theta^4-102\theta^3-2675\theta^2-3688\theta-1502\right)+2^{98} x^{12}\left(10\theta^4+408\theta^3+1273\theta^2+1278\theta+431\right)-2^{108} x^{13}\left(4\theta^4+68\theta^3+179\theta^2+175\theta+59\right)+2^{116} x^{14}(5\theta^2+22\theta+22)(\theta+1)^2-2^{125} x^{15}(\theta+1)^2(\theta+2)^2\)

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Coefficients of the holomorphic solution: 1, -112, 25872, -5691136, 1522998544, ...
--> OEIS
Normalized instanton numbers (n0=1): 800, -121088, 38825120, -15641910336, 7303803435104, ... ; Common denominator:...

Discriminant

\(-(512z+1)(65536z^2-256z-1)(256z+1)^2(67108864z^3+1792z+1)^2(256z-1)^4\)

Local exponents

\(-\frac{ 1}{ 256}\)\(\frac{ 1}{ 512}-\frac{ 1}{ 512}\sqrt{ 5}\)\(-\frac{ 1}{ 512}\) ≈\(-0.000552\)\(0\) ≈\(0.000276-0.00519I\) ≈\(0.000276+0.00519I\)\(\frac{ 1}{ 256}\)\(\frac{ 1}{ 512}+\frac{ 1}{ 512}\sqrt{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(\frac{ 1}{ 2}\)\(1\)\(1\)\(3\)\(0\)\(3\)\(3\)\(1\)\(1\)\(2\)
\(1\)\(2\)\(2\)\(4\)\(0\)\(4\)\(4\)\(2\)\(2\)\(2\)

Note:

This is operator "15.1" from ...

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