1
New Number: 4.48 | AESZ: 241 | Superseeker: 320 19748928 | Hash: b4d16d8dd1eb7839630ecf8e8d242023
Degree: 4
\(\theta^4-2^{4} x\left(152\theta^4+160\theta^3+110\theta^2+30\theta+3\right)+2^{10} 3 x^{2}\left(428\theta^4+176\theta^3-299\theta^2-170\theta-25\right)-2^{17} 3^{2} x^{3}\left(136\theta^4-216\theta^3-180\theta^2-51\theta-5\right)-2^{24} 3^{3} x^{4}(3\theta+1)(2\theta+1)^2(3\theta+2)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 48, 26640, 21907200, 22048765200, ... --> OEIS Normalized instanton numbers (n0=1): 320, 61084, 19748928, 9428973876, 5618509433280, ... ; Common denominator:...
\(-(64z+1)(1728z-1)(-1+384z)^2\)
| \(-\frac{ 1}{ 64}\) | \(0\) | \(\frac{ 1}{ 1728}\) | \(\frac{ 1}{ 384}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 3}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) |
| \(2\) | \(0\) | \(2\) | \(4\) | \(\frac{ 2}{ 3}\) |
2
New Number: 5.32 | AESZ: 215 | Superseeker: 220/3 89212 | Hash: ced61f5675491a3c4446c0e55e7bc36b
Degree: 5
\(3^{2} \theta^4-2^{2} 3 x\left(268\theta^4+632\theta^3+463\theta^2+147\theta+18\right)-2^{7} x^{2}\left(448\theta^4-1616\theta^3-4280\theta^2-2418\theta-441\right)+2^{12} x^{3}\left(416\theta^4+2016\theta^3+756\theta^2-288\theta-135\right)+2^{19} x^{4}(8\theta^2-28\theta-33)(2\theta+1)^2-2^{24} x^{5}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 24, 2664, 470400, 102047400, ... --> OEIS Normalized instanton numbers (n0=1): 220/3, 3538/3, 89212, 7484350, 2459418080/3, ... ; Common denominator:...
\(-(16z-1)(4096z^2-384z+1)(3+64z)^2\)
| \(-\frac{ 3}{ 64}\) | \(0\) | \(\frac{ 3}{ 64}-\frac{ 1}{ 32}\sqrt{ 2}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 3}{ 64}+\frac{ 1}{ 32}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
3
New Number: 8.2 | AESZ: 104 | Superseeker: 7 1271/3 | Hash: d6bd0d1524954c8ce0a6421d295e9795
Degree: 8
\(\theta^4-x(10\theta^2+10\theta+3)(7\theta^2+7\theta+2)-x^{2}\left(71\theta^4+1148\theta^3+1591\theta^2+886\theta+192\right)-2^{3} 3^{2} x^{3}\left(70\theta^4-420\theta^3-1289\theta^2-963\theta-240\right)-2^{4} 3^{2} x^{4}\left(143\theta^4+286\theta^3-1138\theta^2-1281\theta-414\right)+2^{6} 3^{4} x^{5}\left(70\theta^4+700\theta^3+391\theta^2-75\theta-76\right)-2^{6} 3^{4} x^{6}\left(71\theta^4-864\theta^3-1427\theta^2-864\theta-180\right)+2^{9} 3^{6} x^{7}(10\theta^2+10\theta+3)(7\theta^2+7\theta+2)+2^{12} 3^{8} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, 150, 5208, 221094, ... --> OEIS Normalized instanton numbers (n0=1): 7, 93/2, 1271/3, 18507/2, 190710, ... ; Common denominator:...
\((9z+1)(8z-1)(72z-1)(z+1)(1+72z^2)^2\)
| \(-1\) | \(-\frac{ 1}{ 9}\) | \(0-\frac{ 1}{ 12}\sqrt{ 2}I\) | \(0\) | \(0+\frac{ 1}{ 12}\sqrt{ 2}I\) | \(\frac{ 1}{ 72}\) | \(\frac{ 1}{ 8}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(2\) | \(1\) |