Summary

You searched for: dim_h=18

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1

New Number: 5.18 |  AESZ: 124  |  Superseeker: 163/61 4795/61  |  Hash: 394b401a3162e31c79ede5b46973791d  

Degree: 5

\(61^{2} \theta^4-61 x\left(3029\theta^4+5572\theta^3+4677\theta^2+1891\theta+305\right)+x^{2}\left(1215215\theta^4+3428132\theta^3+4267228\theta^2+2572675\theta+611586\right)-3^{4} x^{3}\left(39370\theta^4+140178\theta^3+206807\theta^2+142191\theta+37332\right)+3^{8} x^{4}\left(566\theta^4+2230\theta^3+3356\theta^2+2241\theta+558\right)-3^{13} x^{5}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 5, 69, 1427, 35749, ...
--> OEIS
Normalized instanton numbers (n0=1): 163/61, 630/61, 4795/61, 48422/61, 599809/61, ... ; Common denominator:...

Discriminant

\(-(243z^3-200z^2+47z-1)(-61+81z)^2\)

Local exponents

\(0\) ≈\(0.023574\) ≈\(0.399736-0.121575I\) ≈\(0.399736+0.121575I\)\(\frac{ 61}{ 81}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(3\)\(1\)
\(0\)\(2\)\(2\)\(2\)\(4\)\(1\)

Note:

This is operator "5.18" from ...

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2

New Number: 5.79 |  AESZ: 310  |  Superseeker: 181/11 47171/11  |  Hash: 2b9b103b1c8f0d3175cd1fb9ef5aacc2  

Degree: 5

\(11^{2} \theta^4-11 x\left(1673\theta^4+3046\theta^3+2337\theta^2+814\theta+110\right)+2 5 x^{2}\left(19247\theta^4+28298\theta^3+13285\theta^2+3454\theta+660\right)-2^{2} x^{3}\left(167497\theta^4+245982\theta^3+227451\theta^2+115434\theta+22968\right)+2^{3} 5^{2} x^{4}\left(4079\theta^4+10270\theta^3+11427\theta^2+6226\theta+1340\right)-2^{5} 5^{4} x^{5}(4\theta+3)(\theta+1)^2(4\theta+5)\)

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Coefficients of the holomorphic solution: 1, 10, 450, 30772, 2551810, ...
--> OEIS
Normalized instanton numbers (n0=1): 181/11, 2018/11, 47171/11, 3261479/22, 69313270/11, ... ; Common denominator:...

Discriminant

\(-(z-1)(128z^2-142z+1)(-11+50z)^2\)

Local exponents

\(0\)\(\frac{ 71}{ 128}-\frac{ 17}{ 128}\sqrt{ 17}\)\(\frac{ 11}{ 50}\)\(1\)\(\frac{ 71}{ 128}+\frac{ 17}{ 128}\sqrt{ 17}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 4}\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(4\)\(2\)\(2\)\(\frac{ 5}{ 4}\)

Note:

This is operator "5.79" from ...

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3

New Number: 8.12 |  AESZ: 175  |  Superseeker: 17 1387  |  Hash: f6db11b5e593983f455489d5bb1003c5  

Degree: 8

\(\theta^4-x(10\theta^2+10\theta+3)(17\theta^2+17\theta+6)+3^{4} x^{2}\left(89\theta^4+452\theta^3+633\theta^2+362\theta+80\right)+2^{3} 3^{4} x^{3}\left(170\theta^4-1020\theta^3-3119\theta^2-2373\theta-648\right)-2^{4} 3^{8} x^{4}\left(97\theta^4+194\theta^3-238\theta^2-335\theta-114\right)+2^{6} 3^{8} x^{5}\left(170\theta^4+1700\theta^3+961\theta^2-125\theta-204\right)+2^{6} 3^{12} x^{6}\left(89\theta^4-96\theta^3-189\theta^2-96\theta-12\right)-2^{9} 3^{12} x^{7}(10\theta^2+10\theta+3)(17\theta^2+17\theta+6)+2^{12} 3^{16} x^{8}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 18, 630, 29016, 1529766, ...
--> OEIS
Normalized instanton numbers (n0=1): 17, -299/4, 1387, -47623/2, 500282, ... ; Common denominator:...

Discriminant

\((81z-1)(8z-1)(72z-1)(9z-1)(-1+648z^2)^2\)

Local exponents

\(-\frac{ 1}{ 36}\sqrt{ 2}\)\(0\)\(\frac{ 1}{ 81}\)\(\frac{ 1}{ 72}\)\(\frac{ 1}{ 36}\sqrt{ 2}\)\(\frac{ 1}{ 9}\)\(\frac{ 1}{ 8}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(3\)\(0\)\(1\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(4\)\(0\)\(2\)\(2\)\(4\)\(2\)\(2\)\(1\)

Note:

Hadamard product $c \ast g$. This operator has a second MUM-point
at infinity with the same instanton numbers. It can be reduced to an operator of degree 4 with a single MUM-point defined over $Q(\sqrt{?})$.

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4

New Number: 8.5 |  AESZ: 173  |  Superseeker: 11 -2434/3  |  Hash: afa82ed9ee239bb5fcac960f8884db01  

Degree: 8

\(\theta^4-x(7\theta^2+7\theta+2)(17\theta^2+17\theta+6)+2^{6} x^{2}\left(55\theta^4+112\theta^3+155\theta^2+86\theta+15\right)-2^{6} 3^{2} x^{3}\left(119\theta^4-714\theta^3-2185\theta^2-1656\theta-444\right)+2^{12} 3^{2} x^{4}\left(92\theta^4+184\theta^3+98\theta^2+6\theta+9\right)+2^{12} 3^{4} x^{5}\left(119\theta^4+1190\theta^3+671\theta^2-96\theta-140\right)+2^{18} 3^{4} x^{6}\left(55\theta^4+108\theta^3+149\theta^2+108\theta+27\right)+2^{18} 3^{6} x^{7}(7\theta^2+7\theta+2)(17\theta^2+17\theta+6)+2^{24} 3^{8} x^{8}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 12, 420, 17472, 828324, ...
--> OEIS
Normalized instanton numbers (n0=1): 11, 229/4, -2434/3, 7512, 54801, ... ; Common denominator:...

Discriminant

\((72z-1)(8z+1)(64z-1)(9z+1)(1+576z^2)^2\)

Local exponents

\(-\frac{ 1}{ 8}\)\(-\frac{ 1}{ 9}\)\(0-\frac{ 1}{ 24}I\)\(0\)\(0+\frac{ 1}{ 24}I\)\(\frac{ 1}{ 72}\)\(\frac{ 1}{ 64}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(3\)\(1\)\(1\)\(1\)
\(2\)\(2\)\(4\)\(0\)\(4\)\(2\)\(2\)\(1\)

Note:

Hadamard product $a \ast g$. This operator has a second MUM-point at infinity with the same instanton numbers.
It can be reduced to an operator of degree 4 with a single MUM-point defined over
$Q(\sqrt{?})$.

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