Summary

You searched for: sol=88

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1

New Number: 5.28 |  AESZ: 203  |  Superseeker: -13/5 -6729/5  |  Hash: dfab012366b4bc6f7af83dc79f28b802  

Degree: 5

\(5^{2} \theta^4+5 x\theta(499\theta^3+86\theta^2+53\theta+10)+2^{4} x^{2}\left(1649\theta^4-13183\theta^3-19776\theta^2-11020\theta-2200\right)-2^{6} x^{3}\left(39521\theta^4+162000\theta^3+142095\theta^2+51540\theta+6540\right)-2^{11} 19 x^{4}\left(1370\theta^4+2860\theta^3+2449\theta^2+1019\theta+174\right)-2^{16} 19^{2} x^{5}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 0, 88, -1728, 99576, ...
--> OEIS
Normalized instanton numbers (n0=1): -13/5, 427/5, -6729/5, 173044/5, -952275, ... ; Common denominator:...

Discriminant

\(-(32z-1)(32z^2+71z+1)(5+152z)^2\)

Local exponents

\(-\frac{ 71}{ 64}-\frac{ 17}{ 64}\sqrt{ 17}\)\(-\frac{ 5}{ 152}\)\(-\frac{ 71}{ 64}+\frac{ 17}{ 64}\sqrt{ 17}\)\(0\)\(\frac{ 1}{ 32}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)
\(1\)\(3\)\(1\)\(0\)\(1\)\(1\)
\(2\)\(4\)\(2\)\(0\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding to Operator AESZ 202 /5.27

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2

New Number: 13.13 |  AESZ:  |  Superseeker: 32 74144  |  Hash: e20067c633b6371dc19f760a1140f0e4  

Degree: 13

\(\theta^4-2^{3} x\left(74\theta^4+52\theta^3+70\theta^2+44\theta+11\right)+2^{6} x^{2}\left(1948\theta^4+2320\theta^3+3750\theta^2+3244\theta+1117\right)-2^{11} x^{3}\left(5498\theta^4+9708\theta^3+17699\theta^2+12099\theta+2024\right)+2^{12} x^{4}\left(90192\theta^4+243456\theta^3+317216\theta^2-2080\theta-132883\right)+2^{16} x^{5}\left(35024\theta^4+171680\theta^3+1168736\theta^2+2029296\theta+1162051\right)-2^{20} x^{6}\left(249200\theta^4+1529280\theta^3+3887240\theta^2+5111280\theta+2830091\right)+2^{24} x^{7}\left(6224\theta^4+297952\theta^3+1078344\theta^2+1331848\theta+442349\right)+2^{29} x^{8}\left(78896\theta^4+725696\theta^3+2501496\theta^2+3908720\theta+2314163\right)+2^{34} x^{9}\left(9584\theta^4+62208\theta^3+120960\theta^2+36216\theta-71103\right)+2^{38} x^{10}\left(2864\theta^4+44992\theta^3+291624\theta^2+843472\theta+893907\right)-2^{42} x^{11}\left(8176\theta^4+131296\theta^3+780536\theta^2+2035976\theta+1968867\right)-2^{47} 3 x^{12}\left(752\theta^4+11328\theta^3+62952\theta^2+153648\theta+139383\right)-2^{52} 3^{2} x^{13}\left((2\theta+7)^4\right)\)

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Coefficients of the holomorphic solution: 1, 88, 6576, 475776, 37804816, ...
--> OEIS
Normalized instanton numbers (n0=1): 32, 1048, 74144, 7046865, 788076384, ... ; Common denominator:...

Discriminant

\(-(16z-1)(262144z^4-8192z^3+2304z^2-256z+1)(48z-1)^2(16z+1)^2(512z^2+128z-1)^2\)

Local exponents

\(-\frac{ 1}{ 8}-\frac{ 3}{ 32}\sqrt{ 2}\)\(-\frac{ 1}{ 16}\) ≈\(-0.024399\) ≈\(-0.024399\)\(0\) ≈\(0.004052\)\(-\frac{ 1}{ 8}+\frac{ 3}{ 32}\sqrt{ 2}\)\(\frac{ 1}{ 48}\)\(\frac{ 1}{ 16}\) ≈\(0.075996\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 7}{ 2}\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 7}{ 2}\)
\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(1\)\(3\)\(-2\)\(1\)\(1\)\(\frac{ 7}{ 2}\)
\(4\)\(1\)\(2\)\(2\)\(0\)\(2\)\(4\)\(3\)\(2\)\(2\)\(\frac{ 7}{ 2}\)

Note:

This is operator "13.13" from ...

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