Summary

You searched for: sol=51

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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: 5.68 |  AESZ: 279  |  Superseeker: -10/17 10  |  Hash: 06f80606fbeb2b0cc9559df633f1f59d  

Degree: 5

\(17^{2} \theta^4+17 x\left(286\theta^4+734\theta^3+656\theta^2+289\theta+51\right)+3^{2} x^{2}\left(4110\theta^4+22074\theta^3+37209\theta^2+26265\theta+6800\right)-3^{5} x^{3}\left(1521\theta^4+7344\theta^3+12936\theta^2+9945\theta+2822\right)+3^{8} x^{4}\left(123\theta^4+552\theta^3+879\theta^2+603\theta+152\right)-3^{12} x^{5}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, -3, 9, 51, -1431, ...
--> OEIS
Normalized instanton numbers (n0=1): -10/17, -19/17, 10, -369/17, -1413/17, ... ; Common denominator:...

Discriminant

\(-(729z^3-189z^2-20z-1)(-17+27z)^2\)

Local exponents

≈\(-0.044921-0.04372I\) ≈\(-0.044921+0.04372I\)\(0\) ≈\(0.349102\)\(\frac{ 17}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 280/5.69

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3

New Number: 8.58 |  AESZ:  |  Superseeker: 286 12179050/3  |  Hash: 870f2e78b48eb5ee8f5de2f6a438f2b8  

Degree: 8

\(\theta^4-x\left(1114\theta^4+2444\theta^3+1704\theta^2+482\theta+51\right)-x^{2}\left(85922\theta^4+94748\theta^3-21782\theta^2-21164\theta-3273\right)-3^{2} x^{3}\left(173242\theta^4+41004\theta^3+55912\theta^2+32322\theta+5679\right)+3^{2} x^{4}\left(189512\theta^4-918380\theta^3-841954\theta^2-306732\theta-47331\right)+3^{4} x^{5}\left(30338\theta^4+90716\theta^3-87560\theta^2-90566\theta-23193\right)-3^{4} x^{6}\left(19406\theta^4-68364\theta^3-62162\theta^2-14148\theta+1989\right)-3^{6} 5 x^{7}\left(278\theta^4+340\theta^3+8\theta^2-162\theta-63\right)-3^{8} 5^{2} x^{8}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 51, 18267, 10280301, 7092708939, ...
--> OEIS
Normalized instanton numbers (n0=1): 286, 38919/2, 12179050/3, 2393489451/2, 439227114444, ... ; Common denominator:...

Discriminant

\(-(z+1)(81z^3+549z^2+1187z-1)(-1-36z+45z^2)^2\)

Local exponents

≈\(-3.38931-1.781181I\) ≈\(-3.38931+1.781181I\)\(-1\)\(\frac{ 2}{ 5}-\frac{ 1}{ 15}\sqrt{ 41}\)\(0\) ≈\(0.000842\)\(\frac{ 2}{ 5}+\frac{ 1}{ 15}\sqrt{ 41}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(1\)\(3\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(2\)\(4\)\(0\)\(2\)\(4\)\(1\)

Note:

This is operator "8.58" from ...

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