1
New Number: 6.14 | AESZ: | Superseeker: 8 9928/3 | Hash: 44968de144621e2fa74ce3964a5435f7
Degree: 6
\(\theta^4-2^{2} x(5\theta^2+5\theta+2)(13\theta^2+13\theta+3)+2^{5} x^{2}\left(533\theta^4+2132\theta^3+3137\theta^2+2010\theta+432\right)-2^{8} 3 x^{3}\left(652\theta^4+3912\theta^3+8229\theta^2+7083\theta+1845\right)+2^{12} 3^{2} x^{4}\left(204\theta^4+1632\theta^3+4449\theta^2+4740\theta+1400\right)-2^{15} 3^{3} x^{5}(16\theta^2+80\theta+35)(2\theta+5)^2+2^{17} 3^{4} x^{6}(2\theta+11)(2\theta+7)(2\theta+5)(2\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 24, 1224, 96000, 9633960, ... --> OEIS Normalized instanton numbers (n0=1): 8, 471/2, 9928/3, 185385, 6071232, ... ; Common denominator:...
\((12z-1)(24z-1)(2304z^2-192z+1)(-1+16z)^2\)
| \(0\) | \(\frac{ 1}{ 24}-\frac{ 1}{ 48}\sqrt{ 3}\) | \(\frac{ 1}{ 24}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 24}+\frac{ 1}{ 48}\sqrt{ 3}\) | \(\frac{ 1}{ 12}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(0\) | \(2\) | \(2\) | \(1\) | \(2\) | \(2\) | \(\frac{ 11}{ 2}\) |
2
New Number: 8.88 | AESZ: | Superseeker: 571/15 394769/15 | Hash: 96ea6b0b71373481f874100af7f89d67
Degree: 8
\(3^{2} 5^{2} \theta^4-3 5 x\left(4063\theta^4+7682\theta^3+5731\theta^2+1890\theta+240\right)+2 x^{2}\left(605228\theta^4+1651274\theta^3+1743713\theta^2+827790\theta+149520\right)-2^{2} x^{3}\left(122453\theta^4+9232248\theta^3+20066474\theta^2+11895930\theta+2347980\right)-2^{3} x^{4}\left(14154736\theta^4-3374404\theta^3-69996921\theta^2-57156850\theta-13566428\right)+2^{4} x^{5}\left(30476536\theta^4+168961384\theta^3-11782973\theta^2-90041748\theta-28710648\right)+2^{6} 23 x^{6}\left(1194624\theta^4-7988712\theta^3-9497764\theta^2-3726021\theta-451296\right)-2^{8} 7 23^{2} x^{7}(2\theta+1)(8454\theta^3+5577\theta^2-4303\theta-3155)+2^{10} 7^{2} 23^{3} x^{8}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 1224, 146320, 21334600, ... --> OEIS Normalized instanton numbers (n0=1): 571/15, 3038/5, 394769/15, 23541584/15, 352406944/3, ... ; Common denominator:...
\((1-261z+2952z^2-12368z^3+23552z^4)(-15+74z+1288z^2)^2\)
| \(0\) | \(s_1\) | \(s_3\) | \(s_2\) | \(s_5\) | \(s_4\) | \(s_6\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 3}{ 4}\) |
| \(0\) | \(3\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) | \(\frac{ 5}{ 4}\) |
| \(0\) | \(4\) | \(2\) | \(4\) | \(2\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |