1
New Number: 5.12 | AESZ: 74 | Superseeker: -30 -14632 | Hash: e668180adb7c88d4e5fbab5eb7ee61c7
Degree: 5
\(\theta^4-2 3 x\left(99\theta^4+36\theta^3+39\theta^2+21\theta+4\right)+2^{2} 3^{2} x^{2}\left(3807\theta^4+3564\theta^3+3798\theta^2+1683\theta+284\right)-2^{3} 3^{5} x^{3}\left(7857\theta^4+13608\theta^3+14562\theta^2+7317\theta+1444\right)+2^{4} 3^{9} x^{4}\left(2592\theta^4+7128\theta^3+8550\theta^2+4851\theta+1052\right)-2^{5} 3^{13} x^{5}(3\theta+2)(3\theta+4)(6\theta+5)(6\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 24, 1152, 71520, 5101200, ... --> OEIS Normalized instanton numbers (n0=1): -30, -516, -14632, -4227807/8, -22139868, ... ; Common denominator:...
\(-(-1+54z)(162z-1)^2(108z-1)^2\)
| \(0\) | \(\frac{ 1}{ 162}\) | \(\frac{ 1}{ 108}\) | \(\frac{ 1}{ 54}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 5}{ 6}\) |
| \(0\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 7}{ 6}\) |
| \(0\) | \(4\) | \(1\) | \(2\) | \(\frac{ 4}{ 3}\) |
2
New Number: 8.12 | AESZ: 175 | Superseeker: 17 1387 | Hash: f6db11b5e593983f455489d5bb1003c5
Degree: 8
\(\theta^4-x(10\theta^2+10\theta+3)(17\theta^2+17\theta+6)+3^{4} x^{2}\left(89\theta^4+452\theta^3+633\theta^2+362\theta+80\right)+2^{3} 3^{4} x^{3}\left(170\theta^4-1020\theta^3-3119\theta^2-2373\theta-648\right)-2^{4} 3^{8} x^{4}\left(97\theta^4+194\theta^3-238\theta^2-335\theta-114\right)+2^{6} 3^{8} x^{5}\left(170\theta^4+1700\theta^3+961\theta^2-125\theta-204\right)+2^{6} 3^{12} x^{6}\left(89\theta^4-96\theta^3-189\theta^2-96\theta-12\right)-2^{9} 3^{12} x^{7}(10\theta^2+10\theta+3)(17\theta^2+17\theta+6)+2^{12} 3^{16} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 18, 630, 29016, 1529766, ... --> OEIS Normalized instanton numbers (n0=1): 17, -299/4, 1387, -47623/2, 500282, ... ; Common denominator:...
\((81z-1)(8z-1)(72z-1)(9z-1)(-1+648z^2)^2\)
| \(-\frac{ 1}{ 36}\sqrt{ 2}\) | \(0\) | \(\frac{ 1}{ 81}\) | \(\frac{ 1}{ 72}\) | \(\frac{ 1}{ 36}\sqrt{ 2}\) | \(\frac{ 1}{ 9}\) | \(\frac{ 1}{ 8}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(0\) | \(2\) | \(2\) | \(4\) | \(2\) | \(2\) | \(1\) |
3
New Number: 8.5 | AESZ: 173 | Superseeker: 11 -2434/3 | Hash: afa82ed9ee239bb5fcac960f8884db01
Degree: 8
\(\theta^4-x(7\theta^2+7\theta+2)(17\theta^2+17\theta+6)+2^{6} x^{2}\left(55\theta^4+112\theta^3+155\theta^2+86\theta+15\right)-2^{6} 3^{2} x^{3}\left(119\theta^4-714\theta^3-2185\theta^2-1656\theta-444\right)+2^{12} 3^{2} x^{4}\left(92\theta^4+184\theta^3+98\theta^2+6\theta+9\right)+2^{12} 3^{4} x^{5}\left(119\theta^4+1190\theta^3+671\theta^2-96\theta-140\right)+2^{18} 3^{4} x^{6}\left(55\theta^4+108\theta^3+149\theta^2+108\theta+27\right)+2^{18} 3^{6} x^{7}(7\theta^2+7\theta+2)(17\theta^2+17\theta+6)+2^{24} 3^{8} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 420, 17472, 828324, ... --> OEIS Normalized instanton numbers (n0=1): 11, 229/4, -2434/3, 7512, 54801, ... ; Common denominator:...
\((72z-1)(8z+1)(64z-1)(9z+1)(1+576z^2)^2\)
| \(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 9}\) | \(0-\frac{ 1}{ 24}I\) | \(0\) | \(0+\frac{ 1}{ 24}I\) | \(\frac{ 1}{ 72}\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(2\) | \(1\) |