Summary

You searched for: inst=-20

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1

New Number: 4.29 |  AESZ: 255  |  Superseeker: -20 -28820/3  |  Hash: 86173b300ea0aef95c3f2b60ce5ecf91  

Degree: 4

\(\theta^4+2^{2} x\left(256\theta^4+512\theta^3+653\theta^2+397\theta+94\right)+2^{7} x^{2}\left(3072\theta^4+12288\theta^3+22696\theta^2+20816\theta+7749\right)+2^{12} x^{3}\left(16384\theta^4+98304\theta^3+237760\theta^2+270912\theta+120731\right)+2^{22} x^{4}(4\theta+7)(4\theta+9)(8\theta+15)(8\theta+17)\)

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Coefficients of the holomorphic solution: 1, -376, 117736, -34499456, 9771980456, ...
--> OEIS
Normalized instanton numbers (n0=1): -20, 295, -28820/3, 454190, -26517920, ... ; Common denominator:...

Discriminant

\((256z+1)^4\)

Local exponents

\(-\frac{ 1}{ 256}\)\(0\)\(\infty\)
\(-\frac{ 3}{ 8}\)\(0\)\(\frac{ 7}{ 4}\)
\(\frac{ 3}{ 8}\)\(0\)\(\frac{ 15}{ 8}\)
\(-\frac{ 5}{ 8}\)\(0\)\(\frac{ 17}{ 8}\)
\(-\frac{ 11}{ 8}\)\(0\)\(\frac{ 9}{ 4}\)

Note:

Sporadic YY-Operator.
Can be reduced to 2.70, so not primary operator.

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2

New Number: 4.3 |  AESZ:  |  Superseeker: -20 5924  |  Hash: 4163e7dfeb4b46f62bda072d071020fc  

Degree: 4

\(\theta^4-2^{2} x\left(112\theta^4+224\theta^3+271\theta^2+159\theta+36\right)+2^{6} x^{2}\left(1432\theta^4+5728\theta^3+10849\theta^2+10242\theta+3888\right)-2^{8} 3^{4} x^{3}(112\theta^2+336\theta+341)(2\theta+3)^2+2^{14} 3^{8} x^{4}(\theta+2)^2(2\theta+3)(2\theta+5)\)

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Coefficients of the holomorphic solution: 1, 144, 13320, 432320, -127603800, ...
--> OEIS
Normalized instanton numbers (n0=1): -20, 199, 5924, 82010, -1170848, ... ; Common denominator:...

Discriminant

\((1-224z+20736z^2)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 7}{ 1296}-\frac{ 1}{ 324}\sqrt{ 2}I\)\(\frac{ 7}{ 1296}+\frac{ 1}{ 324}\sqrt{ 2}I\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(2\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(2\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to AESZ 150=$ A \ast \delta $

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3

New Number: 8.45 |  AESZ:  |  Superseeker: -12/5 -20  |  Hash: 52e4f6959f297529016ddef66a399c12  

Degree: 8

\(5^{2} \theta^4+2^{2} 5 x\left(19\theta^4+86\theta^3+73\theta^2+30\theta+5\right)+2^{4} x^{2}\left(709\theta^4+4252\theta^3+7339\theta^2+4830\theta+1165\right)-2^{8} x^{3}\left(420\theta^4+114\theta^3-3294\theta^2-3960\theta-1325\right)-2^{10} x^{4}\left(949\theta^4+6782\theta^3+11350\theta^2+7719\theta+1889\right)+2^{12} x^{5}\left(1315\theta^4+4282\theta^3+7199\theta^2+5744\theta+1691\right)+2^{14} x^{6}\left(613\theta^4+1560\theta^3+973\theta^2-216\theta-249\right)+2^{18} x^{7}\left(11\theta^4-2\theta^3-40\theta^2-39\theta-11\right)-2^{20} x^{8}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, -4, -4, 464, -4244, ...
--> OEIS
Normalized instanton numbers (n0=1): -12/5, -83/5, -20, 3941/20, -13872/5, ... ; Common denominator:...

Discriminant

\(-(8z+1)(128z^3-624z^2-20z-1)(-5+32z+32z^2)^2\)

Local exponents

\(-\frac{ 1}{ 2}-\frac{ 1}{ 8}\sqrt{ 26}\)\(-\frac{ 1}{ 8}\) ≈\(-0.016083-0.036516I\) ≈\(-0.016083+0.036516I\)\(0\)\(-\frac{ 1}{ 2}+\frac{ 1}{ 8}\sqrt{ 26}\) ≈\(4.907166\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(1\)\(1\)\(0\)\(3\)\(1\)\(1\)
\(4\)\(2\)\(2\)\(2\)\(0\)\(4\)\(2\)\(1\)

Note:

This is operator "8.45" from ...

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4

New Number: 2.71 |  AESZ:  |  Superseeker: 0 0  |  Hash: 757b011780c5986bd45a5bf434c76c28  

Degree: 2

\(\theta^4-2^{5} x(2\theta+1)^2(2\theta^2+2\theta+1)+2^{8} x^{2}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, 32, 2160, 181760, 17021200, ...
--> OEIS
Normalized instanton numbers (n0=1): 0, -20, 0, -865, 0, ... ; Common denominator:...

Discriminant

\((-1+128z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 128}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(\frac{ 1}{ 4}\)\(\frac{ 3}{ 4}\)
\(0\)\(\frac{ 3}{ 4}\)\(\frac{ 5}{ 4}\)
\(0\)\(1\)\(\frac{ 3}{ 2}\)

Note:

This is operator is equivalent to [2.33]. Transformation:.....

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