1
New Number: 6.31 | AESZ: | Superseeker: 2/3 13/3 | Hash: fcd8db2a3ad7e58151e501b5872652df
Degree: 6
\(3^{6} \theta^4+2 3^{5} x\left(7\theta^2+7\theta+2\right)-2^{2} 3^{4} x^{2}\left(465\theta^4+1860\theta^3+3069\theta^2+2418\theta+752\right)-3^{3} x^{3}(\theta+2)(\theta+1)(19327\theta^2+57981\theta+52674)+2^{5} 3^{2} x^{4}(17298\theta^2+69192\theta+54655)(\theta+2)^2+2^{4} 3^{2} 11 31 251 x^{5}(\theta+1)(\theta+2)(\theta+3)(\theta+4)-2^{3} 11^{2} 251^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -4/3, 196/9, -604/27, 83956/81, ... --> OEIS Normalized instanton numbers (n0=1): 2/3, 5/3, 13/3, 59/3, 119, ... ; Common denominator:...
\(-(11z-3)(22z+3)(1004z^2+66z-9)(251z^2-33z-9)\)
| \(-\frac{ 3}{ 22}\) | \(\frac{ 33}{ 502}-\frac{ 45}{ 502}\sqrt{ 5}\) | \(-\frac{ 33}{ 1004}-\frac{ 45}{ 1004}\sqrt{ 5}\) | \(0\) | \(-\frac{ 33}{ 1004}+\frac{ 45}{ 1004}\sqrt{ 5}\) | \(\frac{ 33}{ 502}+\frac{ 45}{ 502}\sqrt{ 5}\) | \(\frac{ 3}{ 11}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(4\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(5\) |
2
New Number: 7.7 | AESZ: | Superseeker: 2/3 13/3 | Hash: c7abb9c42d46f14955f0f23351082bef
Degree: 7
\(3^{2} \theta^4-2 3 x\left(88\theta^4+110\theta^3+103\theta^2+48\theta+9\right)+2^{2} x^{2}\left(2923\theta^4+6610\theta^3+8041\theta^2+4908\theta+1206\right)-x^{3}\left(123365\theta^4+374814\theta^3+519741\theta^2+346176\theta+89676\right)+2 x^{4}\left(309657\theta^4+1102938\theta^3+1591157\theta^2+1032920\theta+249740\right)-2^{3} 11 x^{5}(\theta+1)(12897\theta^3+35469\theta^2+31181\theta+8042)-2^{3} 11^{2} x^{6}(\theta+1)(\theta+2)(355\theta^2+1047\theta+806)-2^{4} 11^{3} x^{7}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, 56, 636, 8196, ... --> OEIS Normalized instanton numbers (n0=1): 2/3, 5/3, 13/3, 59/3, 119, ... ; Common denominator:...
\(-(11z-1)(4z^2+22z-1)(z^2+11z-1)(-3+22z)^2\)
| \(-\frac{ 11}{ 2}-\frac{ 5}{ 2}\sqrt{ 5}\) | \(-\frac{ 11}{ 4}-\frac{ 5}{ 4}\sqrt{ 5}\) | \(0\) | \(-\frac{ 11}{ 4}+\frac{ 5}{ 4}\sqrt{ 5}\) | \(-\frac{ 11}{ 2}+\frac{ 5}{ 2}\sqrt{ 5}\) | \(\frac{ 1}{ 11}\) | \(\frac{ 3}{ 22}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(2\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(3\) |
3
New Number: 16.5 | AESZ: | Superseeker: 2/3 -3557/81 | Hash: b0d936e56acdf03e3e72e1814442ab50
Degree: 16
\(3^{2} \theta^4+3 x\left(251\theta^4+70\theta^3+54\theta^2+19\theta+2\right)-x^{2}\left(9925\theta^2+13690\theta-2428\theta^3-28363\theta^4+6024\right)+2^{4} x^{3}\left(37199\theta^4-22299\theta^3-73056\theta^2-78543\theta-30497\right)+2^{4} x^{4}\left(412981\theta^4-1074238\theta^3-2419908\theta^2-2290027\theta-697466\right)+2^{6} x^{5}\left(191993\theta^4-5944270\theta^3-10717950\theta^2-7362757\theta-327010\right)-2^{6} x^{6}\left(10616485\theta^4+72432336\theta^3+96362271\theta^2+3620736\theta-59039988\right)-2^{10} x^{7}\left(8460644\theta^4+24423487\theta^3-9938722\theta^2-101499459\theta-93359835\right)-2^{11} x^{8}\left(12789638\theta^4-61790956\theta^3-472388549\theta^2-910406750\theta-561795471\right)+2^{14} x^{9}\left(17249008\theta^4+194008320\theta^3+675401042\theta^2+875629503\theta+302767578\right)+2^{14} 3^{2} x^{10}\left(17651552\theta^4+131260160\theta^3+303001104\theta^2+57460728\theta-358842021\right)+2^{19} 3 x^{11}\left(3093152\theta^4+7407728\theta^3-96718084\theta^2-479745438\theta-596879613\right)-2^{20} 3^{2} x^{12}\left(2426592\theta^4+35398464\theta^3+214634048\theta^2+589589832\theta+596784069\right)-2^{26} 3^{2} x^{13}\left(166976\theta^4+1827328\theta^3+8848858\theta^2+21296171\theta+20263707\right)-2^{26} 3^{3} x^{14}\left(11312\theta^4-272128\theta^3-2642848\theta^2-7506168\theta-6935571\right)+2^{31} 3^{4} x^{15}\left(2240\theta^4+35304\theta^3+198316\theta^2+480714\theta+429057\right)+2^{32} 3^{8} x^{16}\left((2\theta+7)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -2/3, 142/3, -7312/27, 314042/81, ... --> OEIS Normalized instanton numbers (n0=1): 2/3, 76/9, -3557/81, -5159/486, 1429691/729, ... ; Common denominator:...
\(\)
No data for singularities