Summary

You searched for: inst=-135

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1

New Number: 4.12 |  AESZ:  |  Superseeker: -45 7080  |  Hash: 6c95cb50a57e8a1c96a5a4e3e353cb85  

Degree: 4

\(\theta^4-x\left(1188\theta^4+2376\theta^3+2874\theta^2+1686\theta+765/2\right)+x^{2}\left(535086\theta^4+2140344\theta^3+7708527/2\theta^2+3427839\theta+4938345/4\right)-3^{8} 5^{3} x^{3}(33\theta^2+99\theta+100)(2\theta+3)^2+x^{4}922640625/16(2\theta+3)(2\theta+5)(6\theta+11)(6\theta+13)\)

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Coefficients of the holomorphic solution: 1, 765/2, 1009575/8, 627988725/16, 1505754528075/128, ...
--> OEIS
Normalized instanton numbers (n0=1): -45, -135, 7080, 406035, 17168436, ... ; Common denominator:...

Discriminant

\((1-594z+91125z^2)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 11}{ 3375}-\frac{ 2}{ 3375}I\)\(\frac{ 11}{ 3375}+\frac{ 2}{ 3375}I\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 11}{ 6}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 13}{ 6}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-operator equivalent to AESZ $=b \ast h ~B \ast \eta$

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2

New Number: 4.8 |  AESZ:  |  Superseeker: -135 -417685  |  Hash: f5702d0b3fd53e9b80a42c76a335b648  

Degree: 4

\(\theta^4-x\left(1836\theta^4+3672\theta^3+4368\theta^2+2532\theta+1125/2\right)+x^{2}\left(844182\theta^4+3376728\theta^3+10153755/2\theta^2+3400299\theta+3426705/4\right)-x^{3}6561/2(2\theta+3)^2(102\theta^2+306\theta+305)+x^{4}59049/16(2\theta+3)(2\theta+5)(6\theta+11)(6\theta+13)\)

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Coefficients of the holomorphic solution: 1, 1125/2, 3219615/8, 5002535925/16, 32404173968475/128, ...
--> OEIS
Normalized instanton numbers (n0=1): -135, -22815/4, -417685, -78983235/2, -4331084310, ... ; Common denominator:...

Discriminant

\((1-918z+729z^2)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 17}{ 27}-\frac{ 4}{ 9}\sqrt{ 2}\)\(\frac{ 17}{ 27}+\frac{ 4}{ 9}\sqrt{ 2}\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 11}{ 6}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 13}{ 6}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-Operator equivalent to AESZ 53 =$B \ast \gamma \tilde g \ast h$

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