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1

New Number: 4.26 |  AESZ: 60  |  Superseeker: -10 -870  |  Hash: 033b6632bf7cbbfe2a70e1f1eee4bf04  

Degree: 4

\(\theta^4-x\left(248\theta^4+496\theta^3+604\theta^2+356\theta+81\right)+x^{2}\left(18832\theta^4+75328\theta^3+126798\theta^2+102940\theta+33889\right)-2^{3} 3 x^{3}\left(17856\theta^4+107136\theta^3+256985\theta^2+288843\theta+126617\right)+3^{2} x^{4}(24\theta+41)(24\theta+47)(24\theta+49)(24\theta+55)\)

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Coefficients of the holomorphic solution: 1, 81, 13837/2, 1263327/2, 480917043/8, ...
--> OEIS
Normalized instanton numbers (n0=1): -10, -65, -870, -13905, -248910, ... ; Common denominator:...

Discriminant

\((108z-1)^2(16z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 108}\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 41}{ 24}\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 47}{ 24}\)
\(0\)\(1\)\(1\)\(\frac{ 49}{ 24}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 55}{ 24}\)

Note:

Sporadic YY-Operator

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2

New Number: 4.31 |  AESZ:  |  Superseeker: -10 -340  |  Hash: dc534a2a8e7bca49a87c29d9ed4e3ae8  

Degree: 4

\(\theta^4-2 x\left(172\theta^4+344\theta^3+421\theta^2+249\theta+57\right)+2^{2} x^{2}\left(10852\theta^4+43408\theta^3+78043\theta^2+69270\theta+24987\right)-2^{4} 3 x^{3}\left(49536\theta^4+297216\theta^3+712240\theta^2+799248\theta+349521\right)+2^{14} 3^{2} x^{4}(3\theta+5)(3\theta+7)(6\theta+11)(6\theta+13)\)

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Coefficients of the holomorphic solution: 1, 114, 11466, 1123804, 109952106, ...
--> OEIS
Normalized instanton numbers (n0=1): -10, -40, -340, -5820, -114610, ... ; Common denominator:...

Discriminant

\((108z-1)^2(64z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 108}\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 5}{ 3}\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 11}{ 6}\)
\(0\)\(1\)\(1\)\(\frac{ 13}{ 6}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 7}{ 3}\)

Note:

This is operator "4.31" from ...

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