Summary

You searched for: dim_h=33

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1

New Number: 2.64 |  AESZ: 182  |  Superseeker: 1 7  |  Hash: 89ba4729efa82413b33fe6928ff8d2c9  

Degree: 2

\(\theta^4-x\left(43\theta^4+86\theta^3+77\theta^2+34\theta+6\right)+2^{2} 3 x^{2}(\theta+1)^2(6\theta+5)(6\theta+7)\)

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Coefficients of the holomorphic solution: 1, 6, 66, 924, 14850, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, 7/4, 7, 40, 270, ... ; Common denominator:...

Discriminant

\((27z-1)(16z-1)\)

Local exponents

\(0\)\(\frac{ 1}{ 27}\)\(\frac{ 1}{ 16}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 5}{ 6}\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(2\)\(\frac{ 7}{ 6}\)

Note:

This is operator "2.64" from ...

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2

New Number: 5.25 |  AESZ: 198  |  Superseeker: -84/11 -9052/11  |  Hash: a1f924763b047c2720d99cfca5ca63db  

Degree: 5

\(11^{2} \theta^4+7 11 x\left(130\theta^4+266\theta^3+210\theta^2+77\theta+11\right)-x^{2}\left(11198+55253\theta+103725\theta^2+89990\theta^3+32126\theta^4\right)+x^{3}\left(1716+20625\theta+63474\theta^2+74184\theta^3+28723\theta^4\right)-7 x^{4}\left(1135\theta^4+2336\theta^3+1881\theta^2+713\theta+110\right)+7^{2} x^{5}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, -7, 199, -8359, 423751, ...
--> OEIS
Normalized instanton numbers (n0=1): -84/11, 639/11, -9052/11, 189021/11, -4838013/11, ... ; Common denominator:...

Discriminant

\((z^3-159z^2+84z+1)(-11+7z)^2\)

Local exponents

≈\(-0.011648\)\(0\) ≈\(0.541757\)\(\frac{ 11}{ 7}\) ≈\(158.469891\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(3\)\(1\)\(1\)
\(2\)\(0\)\(2\)\(4\)\(2\)\(1\)

Note:

There is a second MUM-point at infinity, corresponding to Operator AESZ 193/5.22

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3

New Number: 5.68 |  AESZ: 279  |  Superseeker: -10/17 10  |  Hash: 06f80606fbeb2b0cc9559df633f1f59d  

Degree: 5

\(17^{2} \theta^4+17 x\left(286\theta^4+734\theta^3+656\theta^2+289\theta+51\right)+3^{2} x^{2}\left(4110\theta^4+22074\theta^3+37209\theta^2+26265\theta+6800\right)-3^{5} x^{3}\left(1521\theta^4+7344\theta^3+12936\theta^2+9945\theta+2822\right)+3^{8} x^{4}\left(123\theta^4+552\theta^3+879\theta^2+603\theta+152\right)-3^{12} x^{5}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, -3, 9, 51, -1431, ...
--> OEIS
Normalized instanton numbers (n0=1): -10/17, -19/17, 10, -369/17, -1413/17, ... ; Common denominator:...

Discriminant

\(-(729z^3-189z^2-20z-1)(-17+27z)^2\)

Local exponents

≈\(-0.044921-0.04372I\) ≈\(-0.044921+0.04372I\)\(0\) ≈\(0.349102\)\(\frac{ 17}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 280/5.69

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