Summary

You searched for: inst=-5408

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1

New Number: 4.49 |  AESZ: 254  |  Superseeker: -5408 -22147077792  |  Hash: 2539c1ff260271c9f7de53e267e2e8cf  

Degree: 4

\(\theta^4-2^{4} x\left(2608\theta^4-544\theta^3-200\theta^2+72\theta+15\right)+2^{15} 3 x^{2}\left(6128\theta^4-208\theta^3+2328\theta^2+452\theta+25\right)-2^{24} 3^{2} 5 x^{3}\left(4592\theta^4+3456\theta^3+2632\theta^2+816\theta+95\right)+2^{38} 3^{3} 5^{2} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)

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Coefficients of the holomorphic solution: 1, 240, 314640, 627244800, 1516001533200, ...
--> OEIS
Normalized instanton numbers (n0=1): -5408, -8033784, -22147077792, -80392290665536, -341267541912723040, ... ; Common denominator:...

Discriminant

\((6912z-1)(4096z-1)(-1+15360z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 15360}\)\(\frac{ 1}{ 6912}\)\(\frac{ 1}{ 4096}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(3\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(0\)\(4\)\(2\)\(2\)\(\frac{ 2}{ 3}\)

Note:

Sporadic Operator.

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2

New Number: 4.64 |  AESZ: 295  |  Superseeker: -5408 -4296119968  |  Hash: e40629f953a095a2a764c68394321139  

Degree: 4

\(\theta^4-2^{4} x\left(816\theta^4-1440\theta^3-904\theta^2-184\theta-17\right)+2^{18} x^{2}\left(80\theta^4-592\theta^3+432\theta^2+164\theta+23\right)+2^{30} x^{3}\left(80\theta^4-384\theta^3-296\theta^2-96\theta-11\right)+2^{45} x^{4}\left((2\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, -272, 93456, 194502400, -587215823600, ...
--> OEIS
Normalized instanton numbers (n0=1): -5408, -3839480, -4296119968, -6482749129792, -11816577914904160, ... ; Common denominator:...

Discriminant

\((8388608z^2+3328z+1)(-1+8192z)^2\)

Local exponents

\(-\frac{ 13}{ 65536}-\frac{ 7}{ 65536}\sqrt{ 7}I\)\(-\frac{ 13}{ 65536}+\frac{ 7}{ 65536}\sqrt{ 7}I\)\(0\)\(s_1\)\(s_2\)\(\frac{ 1}{ 8192}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(3\)\(\frac{ 1}{ 2}\)
\(2\)\(2\)\(0\)\(2\)\(2\)\(4\)\(\frac{ 1}{ 2}\)

Note:

Sporadic Operator. There is a second MUM-point hiding at
infinity, corresponding to Operator AESZ 296/4.65

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