Summary

You searched for: inst=-44

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1

New Number: 2.63 |  AESZ: 84  |  Superseeker: -4 -44  |  Hash: 908b978c0c447d3643c3018c40e7f5d1  

Degree: 2

\(\theta^4-2^{2} x\left(32\theta^4+64\theta^3+63\theta^2+31\theta+6\right)+2^{8} x^{2}(4\theta+3)(\theta+1)^2(4\theta+5)\)

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Coefficients of the holomorphic solution: 1, 24, 936, 43008, 2145960, ...
--> OEIS
Normalized instanton numbers (n0=1): -4, -11, -44, -156, -288, ... ; Common denominator:...

Discriminant

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

Local exponents

\(0\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(\frac{ 3}{ 4}\)
\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)
\(0\)\(1\)\(\frac{ 5}{ 4}\)

Note:

This is operator "2.63" from ...

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2

New Number: 3.26 |  AESZ: 407  |  Superseeker: 2 440  |  Hash: c46d32ba4b3738ba34fe1e6c16e6f242  

Degree: 3

\(\theta^4+2 x\left(132\theta^4+264\theta^3+293\theta^2+161\theta+35\right)+2^{2} 5^{2} x^{2}(\theta+1)^2(228\theta^2+456\theta+335)+2^{6} 5^{4} x^{3}(\theta+1)(\theta+2)(4\theta+5)(4\theta+7)\)

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Coefficients of the holomorphic solution: 1, -70, 5650, -484900, 43071250, ...
--> OEIS
Normalized instanton numbers (n0=1): 2, -44, 440, -4844, 46268, ... ; Common denominator:...

Discriminant

\((64z+1)(1+100z)^2\)

Local exponents

\(-\frac{ 1}{ 64}\)\(-\frac{ 1}{ 100}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(1\)
\(1\)\(-\frac{ 1}{ 2}\)\(0\)\(\frac{ 5}{ 4}\)
\(1\)\(1\)\(0\)\(\frac{ 7}{ 4}\)
\(2\)\(\frac{ 3}{ 2}\)\(0\)\(2\)

Note:

This is operator "3.26" from ...

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3

New Number: 6.2 |  AESZ:  |  Superseeker: -8 -1552/3  |  Hash: fd7b14f2d0f2a78723588771a9b1a984  

Degree: 6

\(\theta^4-x\left(280\theta^4+560\theta^3+686\theta^2+406\theta+93\right)+3 x^{2}\left(9296\theta^4+37184\theta^3+66322\theta^2+58276\theta+20863\right)-2 x^{3}\left(594560\theta^4+3567360\theta^3+8664912\theta^2+9941616\theta+4484205\right)+x^{4}\left(21204736\theta^4+169637888\theta^3+520783424\theta^2+726030592\theta+387696585\right)-2^{3} 3^{2} 5^{2} x^{5}(4\theta+9)(4\theta+11)(4144\theta^2+20720\theta+28335)+2^{4} 3^{4} 5^{4} x^{6}(4\theta+9)(4\theta+11)(4\theta+13)(4\theta+15)\)

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Coefficients of the holomorphic solution: 1, 93, 15717/2, 1345795/2, 473123715/8, ...
--> OEIS
Normalized instanton numbers (n0=1): -8, -44, -1552/3, -8044, -138528, ... ; Common denominator:...

Discriminant

\((100z-1)^2(4z-1)^2(36z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 100}\)\(\frac{ 1}{ 36}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 9}{ 4}\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 11}{ 4}\)
\(0\)\(1\)\(1\)\(1\)\(\frac{ 13}{ 4}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 15}{ 4}\)

Note:

This is operator "6.2" from ...

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