1
New Number: 4.29 | AESZ: 255 | Superseeker: -20 -28820/3 | Hash: 86173b300ea0aef95c3f2b60ce5ecf91
Degree: 4
\(\theta^4+2^{2} x\left(256\theta^4+512\theta^3+653\theta^2+397\theta+94\right)+2^{7} x^{2}\left(3072\theta^4+12288\theta^3+22696\theta^2+20816\theta+7749\right)+2^{12} x^{3}\left(16384\theta^4+98304\theta^3+237760\theta^2+270912\theta+120731\right)+2^{22} x^{4}(4\theta+7)(4\theta+9)(8\theta+15)(8\theta+17)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -376, 117736, -34499456, 9771980456, ... --> OEIS Normalized instanton numbers (n0=1): -20, 295, -28820/3, 454190, -26517920, ... ; Common denominator:...
\((256z+1)^4\)
\(-\frac{ 1}{ 256}\) | \(0\) | \(\infty\) |
---|---|---|
\(-\frac{ 3}{ 8}\) | \(0\) | \(\frac{ 7}{ 4}\) |
\(\frac{ 3}{ 8}\) | \(0\) | \(\frac{ 15}{ 8}\) |
\(-\frac{ 5}{ 8}\) | \(0\) | \(\frac{ 17}{ 8}\) |
\(-\frac{ 11}{ 8}\) | \(0\) | \(\frac{ 9}{ 4}\) |
2
New Number: 4.3 | AESZ: | Superseeker: -20 5924 | Hash: 4163e7dfeb4b46f62bda072d071020fc
Degree: 4
\(\theta^4-2^{2} x\left(112\theta^4+224\theta^3+271\theta^2+159\theta+36\right)+2^{6} x^{2}\left(1432\theta^4+5728\theta^3+10849\theta^2+10242\theta+3888\right)-2^{8} 3^{4} x^{3}(112\theta^2+336\theta+341)(2\theta+3)^2+2^{14} 3^{8} x^{4}(\theta+2)^2(2\theta+3)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 144, 13320, 432320, -127603800, ... --> OEIS Normalized instanton numbers (n0=1): -20, 199, 5924, 82010, -1170848, ... ; Common denominator:...
\((1-224z+20736z^2)^2\)
\(0\) | \(s_1\) | \(s_2\) | \(\frac{ 7}{ 1296}-\frac{ 1}{ 324}\sqrt{ 2}I\) | \(\frac{ 7}{ 1296}+\frac{ 1}{ 324}\sqrt{ 2}I\) | \(\infty\) |
---|---|---|---|---|---|
\(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
\(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(2\) |
\(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
\(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
3
New Number: 8.45 | AESZ: | Superseeker: -12/5 -20 | Hash: 52e4f6959f297529016ddef66a399c12
Degree: 8
\(5^{2} \theta^4+2^{2} 5 x\left(19\theta^4+86\theta^3+73\theta^2+30\theta+5\right)+2^{4} x^{2}\left(709\theta^4+4252\theta^3+7339\theta^2+4830\theta+1165\right)-2^{8} x^{3}\left(420\theta^4+114\theta^3-3294\theta^2-3960\theta-1325\right)-2^{10} x^{4}\left(949\theta^4+6782\theta^3+11350\theta^2+7719\theta+1889\right)+2^{12} x^{5}\left(1315\theta^4+4282\theta^3+7199\theta^2+5744\theta+1691\right)+2^{14} x^{6}\left(613\theta^4+1560\theta^3+973\theta^2-216\theta-249\right)+2^{18} x^{7}\left(11\theta^4-2\theta^3-40\theta^2-39\theta-11\right)-2^{20} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -4, -4, 464, -4244, ... --> OEIS Normalized instanton numbers (n0=1): -12/5, -83/5, -20, 3941/20, -13872/5, ... ; Common denominator:...
\(-(8z+1)(128z^3-624z^2-20z-1)(-5+32z+32z^2)^2\)
\(-\frac{ 1}{ 2}-\frac{ 1}{ 8}\sqrt{ 26}\) | \(-\frac{ 1}{ 8}\) | ≈\(-0.016083-0.036516I\) | ≈\(-0.016083+0.036516I\) | \(0\) | \(-\frac{ 1}{ 2}+\frac{ 1}{ 8}\sqrt{ 26}\) | ≈\(4.907166\) | \(\infty\) |
---|---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
\(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
\(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(1\) |
\(4\) | \(2\) | \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(1\) |
4
New Number: 2.71 | AESZ: | Superseeker: 0 0 | Hash: 757b011780c5986bd45a5bf434c76c28
Degree: 2
\(\theta^4-2^{5} x(2\theta+1)^2(2\theta^2+2\theta+1)+2^{8} x^{2}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 32, 2160, 181760, 17021200, ... --> OEIS Normalized instanton numbers (n0=1): 0, -20, 0, -865, 0, ... ; Common denominator:...
\((-1+128z)^2\)
\(0\) | \(\frac{ 1}{ 128}\) | \(\infty\) |
---|---|---|
\(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
\(0\) | \(\frac{ 1}{ 4}\) | \(\frac{ 3}{ 4}\) |
\(0\) | \(\frac{ 3}{ 4}\) | \(\frac{ 5}{ 4}\) |
\(0\) | \(1\) | \(\frac{ 3}{ 2}\) |