Summary

You searched for: c3=-90

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1

New Number: 5.1 |  AESZ: 17  |  Superseeker: 6/5 118/5  |  Hash: 370d10edbf5900002f79cf6163e106a5  

Degree: 5

\(5^{2} \theta^4-3 5 x\left(51\theta^4+84\theta^3+72\theta^2+30\theta+5\right)+2 3 x^{2}\left(531\theta^4+828\theta^3+541\theta^2+155\theta+15\right)-2 3^{3} x^{3}\left(423\theta^4+2160\theta^3+4399\theta^2+3795\theta+1170\right)+3^{5} x^{4}\left(279\theta^4+1368\theta^3+2270\theta^2+1586\theta+402\right)-3^{10} x^{5}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 3, 27, 381, 6219, ...
--> OEIS
Normalized instanton numbers (n0=1): 6/5, 39/10, 118/5, 1443/10, 6108/5, ... ; Common denominator:...

Discriminant

\(-(27z-1)(27z^2+1)(-5+9z)^2\)

Local exponents

\(0-\frac{ 1}{ 9}\sqrt{ 3}I\)\(0\)\(0+\frac{ 1}{ 9}\sqrt{ 3}I\)\(\frac{ 1}{ 27}\)\(\frac{ 5}{ 9}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(3\)\(1\)
\(2\)\(0\)\(2\)\(2\)\(4\)\(1\)

Note:

There is a second MUM-point at infinity,
corresponding to Operator AESZ 290/5.71
A-Incarnation: diagonal subfamily 1,1,1-section in $P^2 \times P^2 \times P^2$

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2

New Number: 5.76 |  AESZ: 306  |  Superseeker: 73/3 11119  |  Hash: d14307aa38b16c728ee31e5936937c44  

Degree: 5

\(3^{2} \theta^4-3 x\left(592\theta^4+1100\theta^3+829\theta^2+279\theta+36\right)+x^{2}\left(13801\theta^4+6652\theta^3-18041\theta^2-14904\theta-3312\right)-2 x^{3}\theta(8461\theta^3-29160\theta^2-28365\theta-7236)-2^{2} 3 7 x^{4}\left(513\theta^4+864\theta^3+487\theta^2+64\theta-16\right)-2^{3} 3 7^{2} x^{5}(\theta+1)^2(3\theta+2)(3\theta+4)\)

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Coefficients of the holomorphic solution: 1, 12, 732, 67080, 7456140, ...
--> OEIS
Normalized instanton numbers (n0=1): 73/3, 2131/6, 11119, 518671, 29749701, ... ; Common denominator:...

Discriminant

\(-(z+1)(54z^2+189z-1)(-3+14z)^2\)

Local exponents

\(-\frac{ 7}{ 4}-\frac{ 11}{ 36}\sqrt{ 33}\)\(-1\)\(0\)\(-\frac{ 7}{ 4}+\frac{ 11}{ 36}\sqrt{ 33}\)\(\frac{ 3}{ 14}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(\frac{ 4}{ 3}\)

Note:

This is operator "5.76" from ...

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3

New Number: 8.16 |  AESZ: 196  |  Superseeker: 189/47 9277/47  |  Hash: fdeee36c14d9c003b59c1738c024d479  

Degree: 8

\(47^{2} \theta^4-47 x\left(2489\theta^4+4984\theta^3+4043\theta^2+1551\theta+235\right)-x^{2}\left(161022+701851\theta+1135848\theta^2+790072\theta^3+208867\theta^4\right)+x^{3}\left(38352+149319\theta+383912\theta^2+637644\theta^3+370857\theta^4\right)-x^{4}\left(1770676+5161283\theta+4424049\theta^2+511820\theta^3-291161\theta^4\right)+x^{5}\left(2151-260936\theta-750755\theta^2-749482\theta^3-406192\theta^4\right)+3^{3} x^{6}\left(5305\theta^4+90750\theta^3+152551\theta^2+91194\theta+17914\right)+2 3^{6} x^{7}\left(106\theta^4+230\theta^3+197\theta^2+82\theta+15\right)-2^{2} 3^{10} x^{8}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 5, 93, 2507, 81229, ...
--> OEIS
Normalized instanton numbers (n0=1): 189/47, 979/47, 9277/47, 124795/47, 2049020/47, ... ; Common denominator:...

Discriminant

\(-(-1+53z+90z^2-50z^3+81z^4)(-47-z+54z^2)^2\)

Local exponents

\(\frac{ 1}{ 108}-\frac{ 1}{ 108}\sqrt{ 10153}\)\(0\)\(\frac{ 1}{ 108}+\frac{ 1}{ 108}\sqrt{ 10153}\)\(#ND+#NDI\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(1\)
\(3\)\(0\)\(3\)\(1\)\(1\)
\(4\)\(0\)\(4\)\(2\)\(1\)

Note:

The operator has a second MUM-point at infinity, corresponding to operator 8.17 .

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4

New Number: 8.20 |  AESZ: 213  |  Superseeker: 118/17 672  |  Hash: d430b37f4ca641af0b82cbef83547c51  

Degree: 8

\(17^{2} \theta^4-2 17 x\left(647\theta^4+1240\theta^3+977\theta^2+357\theta+51\right)-2^{2} x^{2}\left(14437\theta^4+89752\theta^3+147734\theta^2+92123\theta+20400\right)+2^{2} 3 x^{3}\left(21538\theta^4+25680\theta^3-41979\theta^2-56151\theta-17442\right)+2^{3} x^{4}\left(51920\theta^4+166384\theta^3-83149\theta^2-217017\theta-79362\right)-2^{4} 3 x^{5}\left(9360\theta^4-26784\theta^3-43813\theta^2-21965\theta-3496\right)-2^{5} 3 x^{6}\left(10160\theta^4-96\theta^3-10535\theta^2-5385\theta-438\right)-2^{8} 3^{2} x^{7}\left(288\theta^4+864\theta^3+1082\theta^2+641\theta+147\right)-2^{11} 3^{2} x^{8}(4\theta+3)(\theta+1)^2(4\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 162, 6252, 290610, ...
--> OEIS
Normalized instanton numbers (n0=1): 118/17, 873/17, 672, 447987/34, 5358846/17, ... ; Common denominator:...

Discriminant

\(-(4z+1)(32z^3+40z^2+78z-1)(-17+18z+48z^2)^2\)

Local exponents

\(-\frac{ 3}{ 16}-\frac{ 1}{ 48}\sqrt{ 897}\) ≈\(-0.631368-1.433512I\) ≈\(-0.631368+1.433512I\)\(-\frac{ 1}{ 4}\)\(0\) ≈\(0.012736\)\(-\frac{ 3}{ 16}+\frac{ 1}{ 48}\sqrt{ 897}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 3}{ 4}\)
\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(3\)\(1\)\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(4\)\(2\)\(2\)\(2\)\(0\)\(2\)\(4\)\(\frac{ 5}{ 4}\)

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