1
New Number: 4.23 | AESZ: | Superseeker: -1116 -349462868 | Hash: 4cde44ecce8658b2c2ca6b3c279f4e62
Degree: 4
\(\theta^4-2^{2} 3^{2} x\left(432\theta^4+864\theta^3+1023\theta^2+591\theta+131\right)+2^{4} 3^{5} 5 x^{2}\left(2592\theta^4+10368\theta^3+13788\theta^2+6840\theta+689\right)+2^{8} 3^{14} x^{3}(16\theta^2+48\theta+47)(2\theta+3)^2+2^{14} 3^{16} x^{4}(2\theta+3)(2\theta+5)(3\theta+5)(3\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4716, 31430916, 223425214992, 1654537886846532, ... --> OEIS Normalized instanton numbers (n0=1): -1116, -586989, -349462868, -300569202144, -280354383814176, ... ; Common denominator:...
\((5038848z^2+7776z-1)^2\)
| \(-\frac{ 1}{ 1296}-\frac{ 1}{ 1944}\sqrt{ 3}\) | \(0\) | \(s_1\) | \(s_2\) | \(-\frac{ 1}{ 1296}+\frac{ 1}{ 1944}\sqrt{ 3}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(-\frac{ 1}{ 2}\) | \(0\) | \(0\) | \(0\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 5}{ 3}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 3}\) |
| \(\frac{ 3}{ 2}\) | \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 5}{ 2}\) |
2
New Number: 8.64 | AESZ: | Superseeker: 0 -32768 | Hash: 00b5810e4a2d21fec464e4e87169df86
Degree: 8
\(\theta^4-2^{4} x\left(32\theta^4+16\theta^3+14\theta^2+6\theta+1\right)+2^{10} x^{2}\left(86\theta^4+176\theta^3+184\theta^2+76\theta+13\right)-2^{16} x^{3}\left(61\theta^4+510\theta^3+620\theta^2+327\theta+68\right)-2^{22} x^{4}\left(110\theta^4-260\theta^3-942\theta^2-608\theta-141\right)+2^{26} x^{5}\left(708\theta^4+2160\theta^3-666\theta^2-1230\theta-397\right)+2^{32} x^{6}\left(134\theta^4-1536\theta^3-1488\theta^2-492\theta-29\right)-2^{38} 5 x^{7}\left(73\theta^4+170\theta^3+168\theta^2+83\theta+17\right)-2^{44} 5^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 272, -15104, -2814704, ... --> OEIS Normalized instanton numbers (n0=1): 0, -1116, -32768, -2011784, -92274688, ... ; Common denominator:...
\(-(64z-1)(65536z^3+14336z^2-192z+1)(-1+128z+10240z^2)^2\)
| ≈\(-0.23168\) | \(-\frac{ 1}{ 160}-\frac{ 1}{ 320}\sqrt{ 14}\) | \(0\) | \(-\frac{ 1}{ 160}+\frac{ 1}{ 320}\sqrt{ 14}\) | ≈\(0.006465-0.004906I\) | ≈\(0.006465+0.004906I\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(2\) | \(2\) | \(1\) |