1
New Number: 5.21 | AESZ: 187 | Superseeker: -107 -121311 | Hash: 9a367922f464a13fa56d1c2e238faa34
Degree: 5
\(\theta^4-x\left(64\theta^4-898\theta^3-653\theta^2-204\theta-27\right)-3^{2} x^{2}\left(6397\theta^4+13390\theta^3-10135\theta^2-7492\theta-1650\right)+3^{4} x^{3}\left(64745\theta^4-109026\theta^3-106415\theta^2-39528\theta-4626\right)+3^{9} 19 x^{4}\left(700\theta^4+1562\theta^3+1485\theta^2+704\theta+138\right)-3^{14} 19^{2} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -27, 1971, -220941, 30762099, ... --> OEIS Normalized instanton numbers (n0=1): -107, -7701/4, -121311, -6204874, -518204863, ... ; Common denominator:...
\(-(243z+1)(243z^2-35z-1)(-1+171z)^2\)
| \(\frac{ 35}{ 486}-\frac{ 13}{ 486}\sqrt{ 13}\) | \(-\frac{ 1}{ 243}\) | \(0\) | \(\frac{ 1}{ 171}\) | \(\frac{ 35}{ 486}+\frac{ 13}{ 486}\sqrt{ 13}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(1\) |
2
New Number: 11.19 | AESZ: | Superseeker: 21/4 -1045/6 | Hash: acf903f94ac2a08b9f2b26dff65a52ff
Degree: 11
\(2^{4} \theta^4-2^{2} 3 x\left(42\theta^4+102\theta^3+79\theta^2+28\theta+4\right)+3^{3} x^{2}\left(315\theta^4+4266\theta^3+5903\theta^2+3052\theta+596\right)+3^{6} x^{3}\left(1318\theta^4+2322\theta^3+1973\theta^2+1480\theta+380\right)-3^{8} x^{4}\left(929\theta^4-9440\theta^3-49249\theta^2-40585\theta-10625\right)-3^{10} x^{5}\left(2379\theta^4-3180\theta^3+21452\theta^2+12663\theta+2214\right)-3^{12} x^{6}\left(1180\theta^4+108042\theta^3+173091\theta^2+112103\theta+25380\right)+3^{13} x^{7}\left(27312\theta^4+432678\theta^3+80098\theta^2-241649\theta-108332\right)+3^{15} x^{8}\left(107658\theta^4+438498\theta^3+811975\theta^2+529736\theta+119035\right)-3^{18} x^{9}\left(96469\theta^4+336390\theta^3+294983\theta^2+82398\theta+582\right)+2 3^{20} 13 x^{10}\left(2902\theta^4+5462\theta^3+3737\theta^2+1006\theta+63\right)+2^{2} 3^{23} 13^{2} x^{11}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 3, -27, -1563, -40491, ... --> OEIS Normalized instanton numbers (n0=1): 21/4, -969/16, -1045/6, -35199/4, 536619/4, ... ; Common denominator:...
\((1-36z+1458z^2+18225z^3+761076z^4+177147z^5)(4+9z-1539z^2+18954z^3)^2\)
| ≈\(-4.272671\) | ≈\(-0.039841\) | ≈\(-0.024843\) | ≈\(-0.024843\) | \(0\) | ≈\(0.01303\) | ≈\(0.01303\) | ≈\(0.060519-0.040429I\) | ≈\(0.060519+0.040429I\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(3\) | \(3\) | \(1\) |
| \(2\) | \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(4\) | \(4\) | \(1\) |
3
New Number: 7.17 | AESZ: | Superseeker: 0 18 | Hash: c248fd7c807d0aae71ef687a9ee40c80
Degree: 7
\(\theta^4+3 x\left(87\theta^4+84\theta^3+86\theta^2+44\theta+9\right)+2 3^{3} x^{2}\left(539\theta^4+1076\theta^3+1366\theta^2+880\theta+233\right)+2 3^{5} x^{3}\left(3699\theta^4+11424\theta^3+17579\theta^2+13389\theta+4088\right)+3^{7} x^{4}\left(30367\theta^4+128696\theta^3+235722\theta^2+205070\theta+69226\right)+3^{9} x^{5}\left(74547\theta^4+405660\theta^3+871096\theta^2+848930\theta+310507\right)+2 3^{11} 5 x^{6}(2\theta+3)(5066\theta^3+26325\theta^2+44815\theta+23766)+2^{2} 3^{14} 5^{2} 7^{2} x^{7}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -27, 783, -23481, 717903, ... --> OEIS Normalized instanton numbers (n0=1): 0, -27/2, 18, -999/2, 1566, ... ; Common denominator:...
\((27z+1)(1323z^2+72z+1)(36z+1)^2(45z+1)^2\)
| \(-\frac{ 1}{ 27}\) | \(-\frac{ 1}{ 36}\) | \(-\frac{ 4}{ 147}-\frac{ 1}{ 441}\sqrt{ 3}I\) | \(-\frac{ 4}{ 147}+\frac{ 1}{ 441}\sqrt{ 3}I\) | \(-\frac{ 1}{ 45}\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) | \(0\) | \(\frac{ 5}{ 2}\) |
| \(2\) | \(1\) | \(2\) | \(2\) | \(4\) | \(0\) | \(3\) |