1
New Number: 4.50 | AESZ: 256 | Superseeker: -128 -800384 | Hash: 05e172cfdecc836685981a2b01b75d1d
Degree: 4
\(\theta^4+2^{5} x\left(24\theta^4+42\theta^3+30\theta^2+9\theta+1\right)+2^{8} x^{2}\left(164\theta^4+104\theta^3-144\theta^2-100\theta-17\right)+2^{14} x^{3}\left(28\theta^4-48\theta^3-44\theta^2-12\theta-1\right)-2^{18} x^{4}\left((2\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -32, 7056, -2393600, 991152400, ... --> OEIS Normalized instanton numbers (n0=1): -128, 6884, -800384, 143245314, -31691939200, ... ; Common denominator:...
\(-(4096z^2-704z-1)(1+32z)^2\)
| \(-\frac{ 1}{ 32}\) | \(\frac{ 11}{ 128}-\frac{ 5}{ 128}\sqrt{ 5}\) | \(0\) | \(s_1\) | \(s_2\) | \(\frac{ 11}{ 128}+\frac{ 5}{ 128}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 1}{ 2}\) |
2
New Number: 8.53 | AESZ: | Superseeker: -64 -64320 | Hash: 0714a480e1c587ebada71771f7e3b555
Degree: 8
\(\theta^4-2^{5} x\left(2\theta^4-20\theta^3-16\theta^2-6\theta-1\right)-2^{8} x^{2}\left(80\theta^4+32\theta^3-472\theta^2-336\theta-91\right)-2^{14} x^{3}\left(32\theta^4+576\theta^3-52\theta^2-300\theta-141\right)+2^{20} x^{4}\left(116\theta^4-560\theta^3-768\theta^2-464\theta-91\right)+2^{26} x^{5}\left(220\theta^4+232\theta^3-28\theta^2-220\theta-95\right)+2^{30} x^{6}\left(640\theta^4+2304\theta^3+3752\theta^2+2928\theta+867\right)+2^{36} x^{7}\left(176\theta^4+736\theta^3+1156\theta^2+788\theta+197\right)+2^{46} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -32, 1168, -43520, 1777936, ... --> OEIS Normalized instanton numbers (n0=1): -64, -1604, -64320, -3255802, -191614656, ... ; Common denominator:...
\((1+64z+4096z^2)(64z+1)^2(2048z^2+128z-1)^2\)
| \(-\frac{ 1}{ 32}-\frac{ 1}{ 64}\sqrt{ 6}\) | \(-\frac{ 1}{ 64}\) | \(-\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 3}I\) | \(-\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 3}I\) | \(0\) | \(-\frac{ 1}{ 32}+\frac{ 1}{ 64}\sqrt{ 6}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(3\) | \(1\) |
| \(4\) | \(1\) | \(2\) | \(2\) | \(0\) | \(4\) | \(1\) |