Summary

You searched for: inst=25

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1

New Number: 5.103 |  AESZ: 354  |  Superseeker: 25 17175  |  Hash: 0d4263e8c85dceb5c51f8614f7c1bc79  

Degree: 5

\(\theta^4-5 x\left(170\theta^4+160\theta^3+125\theta^2+45\theta+6\right)+3 5^{3} x^{2}\left(725\theta^4+1220\theta^3+1105\theta^2+460\theta+68\right)-3^{2} 5^{5} x^{3}\left(1421\theta^4+3186\theta^3+3053\theta^2+1272\theta+188\right)+2^{2} 3^{3} 5^{7} x^{4}(3\theta+1)(3\theta+2)(34\theta^2+61\theta+36)-2^{2} 3^{4} 5^{9} x^{5}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)

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Coefficients of the holomorphic solution: 1, 30, 3150, 462000, 78828750, ...
--> OEIS
Normalized instanton numbers (n0=1): 25, 2175/4, 17175, 351250, 23000351/5, ... ; Common denominator:...

Discriminant

\(-(2278125z^3-84375z^2+550z-1)(-1+150z)^2\)

Local exponents

\(0\) ≈\(0.003863-0.000232I\) ≈\(0.003863+0.000232I\)\(\frac{ 1}{ 150}\) ≈\(0.029311\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(1\)\(3\)\(1\)\(\frac{ 4}{ 3}\)
\(0\)\(2\)\(2\)\(4\)\(2\)\(\frac{ 5}{ 3}\)

Note:

This is operator "5.103" from ...

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2

New Number: 6.6 |  AESZ:  |  Superseeker: 25 17452  |  Hash: e97e9b0e87960fe4cffbb22a5e935b4a  

Degree: 6

\(\theta^4-x\left(12+100\theta+305\theta^2+410\theta^3+205\theta^4\right)-2^{5} x^{2}\left(127\theta^4+508\theta^3+742\theta^2+468\theta+99\right)-2^{2} 3 x^{3}\left(2588\theta^4+15528\theta^3+32639\theta^2+28041\theta+7290\right)-2^{6} 3^{2} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)-2^{7} 3^{3} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2-2^{7} 3^{4} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)

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Coefficients of the holomorphic solution: 1, 12, 972, 106200, 14027580, ...
--> OEIS
Normalized instanton numbers (n0=1): 25, 446, 17452, 958347, 65098152, ... ; Common denominator:...

Discriminant

\(-(3z+1)(3456z^3+1728z^2+216z-1)(4z+1)^2\)

Local exponents

\(-\frac{ 1}{ 3}\) ≈\(-0.252234-0.033647I\) ≈\(-0.252234+0.033647I\)\(-\frac{ 1}{ 4}\)\(0\)\(\frac{ 1}{ 12}2^(\frac{ 1}{ 3})+\frac{ 1}{ 24}2^(\frac{ 2}{ 3})-\frac{ 1}{ 6}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(0\)\(1\)\(\frac{ 5}{ 2}\)
\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(0\)\(1\)\(\frac{ 7}{ 2}\)
\(2\)\(2\)\(2\)\(1\)\(0\)\(2\)\(\frac{ 11}{ 2}\)

Note:

This is operator "6.6" from ...

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