Summary

You searched for: sol=288

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1

New Number: 2.61 |  AESZ: 26  |  Superseeker: 10 1724  |  Hash: f3fc09474973b19b8bdb783e3322eb65  

Degree: 2

\(\theta^4-2 x(2\theta+1)^2(13\theta^2+13\theta+4)-2^{2} 3 x^{2}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, 8, 288, 15200, 968800, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, 191/2, 1724, 45680, 1478214, ... ; Common denominator:...

Discriminant

\(-(4z+1)(108z-1)\)

Local exponents

\(-\frac{ 1}{ 4}\)\(0\)\(\frac{ 1}{ 108}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(\frac{ 2}{ 3}\)
\(1\)\(0\)\(1\)\(\frac{ 4}{ 3}\)
\(2\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

A-incarnation: $X(1,1,1,1,2) \subset Grass(2,6)$

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2

New Number: 5.74 |  AESZ: 297  |  Superseeker: 26/7 55644/7  |  Hash: cd0b6008fa6b70d89e004100b5698063  

Degree: 5

\(7^{2} \theta^4-2 7 x\theta(520\theta^3+68\theta^2+41\theta+7)-2^{2} 3 x^{2}\left(9480\theta^4+153912\theta^3+212893\theta^2+108080\theta+18816\right)+2^{4} 3^{3} 7 x^{3}\left(13424\theta^4+48792\theta^3+45656\theta^2+17979\theta+2606\right)-2^{6} 3^{7} x^{4}(2\theta+1)^2(2257\theta^2+3601\theta+1942)+2^{11} 3^{11} x^{5}(2\theta+1)^2(2\theta+3)^2\)

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Coefficients of the holomorphic solution: 1, 0, 288, 7200, 1058400, ...
--> OEIS
Normalized instanton numbers (n0=1): 26/7, 2594/7, 55644/7, 2996576/7, 135364470/7, ... ; Common denominator:...

Discriminant

\((128z-1)(432z^2-72z-1)(-7+324z)^2\)

Local exponents

\(\frac{ 1}{ 12}-\frac{ 1}{ 18}\sqrt{ 3}\)\(0\)\(\frac{ 1}{ 128}\)\(\frac{ 7}{ 324}\)\(\frac{ 1}{ 12}+\frac{ 1}{ 18}\sqrt{ 3}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(3\)\(1\)\(\frac{ 3}{ 2}\)
\(2\)\(0\)\(2\)\(4\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.74" from ...

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3

New Number: 7.1 |  AESZ:  |  Superseeker: 10/7 508/7  |  Hash: 08ab3cb496250adfa30bc3e24ac63c4f  

Degree: 7

\(7^{2} \theta^4-2 7 x\theta(46\theta^3+52\theta^2+33\theta+7)-2^{2} x^{2}\left(7332\theta^4+28848\theta^3+42633\theta^2+26670\theta+6272\right)-2^{4} x^{3}\left(2860\theta^4+44760\theta^3+120483\theta^2+111279\theta+35098\right)+2^{9} x^{4}\left(2230\theta^4+5920\theta^3-741\theta^2-6509\theta-3049\right)+2^{14} x^{5}\left(174\theta^4+1320\theta^3+1971\theta^2+1095\theta+190\right)-2^{19} x^{6}\left(22\theta^4+24\theta^3-9\theta^2-21\theta-7\right)-2^{25} x^{7}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 0, 32, 288, 7776, ...
--> OEIS
Normalized instanton numbers (n0=1): 10/7, 100/7, 508/7, 808, 59910/7, ... ; Common denominator:...

Discriminant

\(-(16z+1)(32z-1)(32z-7)^2(4z+1)^3\)

Local exponents

\(-\frac{ 1}{ 4}\)\(-\frac{ 1}{ 16}\)\(0\)\(\frac{ 1}{ 32}\)\(\frac{ 7}{ 32}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(\frac{ 3}{ 2}\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(0\)\(2\)\(4\)\(1\)

Note:

This is operator "7.1" from ...

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4

New Number: 8.68 |  AESZ:  |  Superseeker: 6/17 33/17  |  Hash: 0c0662f5b46ac6cb0bd298a63cf364c7  

Degree: 8

\(17^{2} \theta^4+17 x\theta(165\theta^3-114\theta^2-74\theta-17)-x^{2}\left(20619\theta^4+122880\theta^3+175353\theta^2+126480\theta+36992\right)-2 x^{3}\left(201857\theta^4+853944\theta^3+1437673\theta^2+1174122\theta+375972\right)-2^{2} x^{4}\left(571275\theta^4+2711616\theta^3+5301571\theta^2+4856674\theta+1694372\right)-2^{3} 3 x^{5}(\theta+1)(295815\theta^3+1523993\theta^2+2924668\theta+1983212)-2^{5} x^{6}(\theta+1)(\theta+2)(558823\theta^2+2951265\theta+4136951)-2^{7} 3 37 x^{7}(\theta+3)(\theta+2)(\theta+1)(2797\theta+9878)-2^{9} 3^{2} 7 37^{2} x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

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Coefficients of the holomorphic solution: 1, 0, 8, 24, 288, ...
--> OEIS
Normalized instanton numbers (n0=1): 6/17, 25/34, 33/17, 157/17, 577/17, ... ; Common denominator:...

Discriminant

\(-(12z-1)(6z+1)(7z^2-z+1)(4z+1)^2(74z+17)^2\)

Local exponents

\(-\frac{ 1}{ 4}\)\(-\frac{ 17}{ 74}\)\(-\frac{ 1}{ 6}\)\(0\)\(\frac{ 1}{ 14}-\frac{ 3}{ 14}\sqrt{ 3}I\)\(\frac{ 1}{ 14}+\frac{ 3}{ 14}\sqrt{ 3}I\)\(\frac{ 1}{ 12}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(\frac{ 1}{ 2}\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(2\)
\(\frac{ 1}{ 2}\)\(3\)\(1\)\(0\)\(1\)\(1\)\(1\)\(3\)
\(1\)\(4\)\(2\)\(0\)\(2\)\(2\)\(2\)\(4\)

Note:

This is operator "8.68" from ...

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