1
New Number: 5.20 | AESZ: 186 | Superseeker: 49/19 1761/19 | Hash: b3d164f22d02de1efcd62d3aa9ab5ce4
Degree: 5
\(19^{2} \theta^4-19 x\left(700\theta^4+1238\theta^3+999\theta^2+380\theta+57\right)-x^{2}\left(64745\theta^4+368006\theta^3+609133\theta^2+412756\theta+102258\right)+3^{3} x^{3}\left(6397\theta^4+12198\theta^3-11923\theta^2-27360\theta-11286\right)+3^{6} x^{4}\left(64\theta^4+1154\theta^3+2425\theta^2+1848\theta+486\right)-3^{11} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 3, 51, 1029, 25299, ... --> OEIS Normalized instanton numbers (n0=1): 49/19, 252/19, 1761/19, 18990/19, 246159/19, ... ; Common denominator:...
\(-(z+1)(243z^2+35z-1)(-19+27z)^2\)
\(-1\) | \(-\frac{ 35}{ 486}-\frac{ 13}{ 486}\sqrt{ 13}\) | \(0\) | \(-\frac{ 35}{ 486}+\frac{ 13}{ 486}\sqrt{ 13}\) | \(\frac{ 19}{ 27}\) | \(\infty\) |
---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) |
\(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(1\) |
2
New Number: 8.26 | AESZ: 301 | Superseeker: 193/11 48570/11 | Hash: a91db18876a9dfbf42b88f8d64c55d85
Degree: 8
\(11^{2} \theta^4-11 x\left(1517\theta^4+3136\theta^3+2393\theta^2+825\theta+110\right)-x^{2}\left(24266+106953\theta+202166\theta^2+207620\theta^3+90362\theta^4\right)-x^{3}\left(53130+217437\theta+415082\theta^2+507996\theta^3+245714\theta^4\right)-x^{4}\left(15226+183269\theta+564786\theta^2+785972\theta^3+407863\theta^4\right)-x^{5}\left(25160+279826\theta+728323\theta^2+790148\theta^3+434831\theta^4\right)-2^{3} x^{6}\left(36361\theta^4+70281\theta^3+73343\theta^2+37947\theta+7644\right)-2^{4} 5 x^{7}\left(1307\theta^4+3430\theta^3+3877\theta^2+2162\theta+488\right)-2^{9} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 10, 466, 32392, 2727826, ... --> OEIS Normalized instanton numbers (n0=1): 193/11, 1973/11, 48570/11, 1689283/11, 72444183/11, ... ; Common denominator:...
\(-(-1+143z+32z^2)(z+1)^2(20z^2+17z+11)^2\)
\(-\frac{ 143}{ 64}-\frac{ 19}{ 64}\sqrt{ 57}\) | \(-1\) | \(-\frac{ 17}{ 40}-\frac{ 1}{ 40}\sqrt{ 591}I\) | \(-\frac{ 17}{ 40}+\frac{ 1}{ 40}\sqrt{ 591}I\) | \(0\) | \(-\frac{ 143}{ 64}+\frac{ 19}{ 64}\sqrt{ 57}\) | \(\infty\) |
---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
\(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
\(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(3\) | \(0\) | \(1\) | \(1\) |
\(2\) | \(1\) | \(4\) | \(4\) | \(0\) | \(2\) | \(1\) |