1
New Number: 6.24 | AESZ: | Superseeker: 1/3 5/3 | Hash: aebe18b25bf886c4483ce54370c0fcbe
Degree: 6
\(3^{6} \theta^4+3^{5} x\left(7\theta^2+7\theta+2\right)-3^{4} x^{2}\left(1095\theta^4+4380\theta^3+7227\theta^2+5694\theta+1760\right)-2 3^{3} x^{3}(\theta+2)(\theta+1)(4165\theta^2+12495\theta+11148)+2^{2} 3^{2} x^{4}(47961\theta^2+191844\theta+148643)(\theta+2)^2+2^{3} 3^{2} 5 7 17 73 x^{5}(\theta+1)(\theta+2)(\theta+3)(\theta+4)-2^{5} 5^{2} 7^{2} 17^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -2/3, 112/9, -8/27, 29500/81, ... --> OEIS Normalized instanton numbers (n0=1): 1/3, 5/6, 5/3, 19/3, 29, ... ; Common denominator:...
\(-(7z-3)(34z-3)(17z+3)(20z+3)(10z-3)(14z+3)\)
| \(-\frac{ 3}{ 14}\) | \(-\frac{ 3}{ 17}\) | \(-\frac{ 3}{ 20}\) | \(0\) | \(\frac{ 3}{ 34}\) | \(\frac{ 3}{ 10}\) | \(\frac{ 3}{ 7}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(4\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(5\) |
2
New Number: 6.31 | AESZ: | Superseeker: 2/3 13/3 | Hash: fcd8db2a3ad7e58151e501b5872652df
Degree: 6
\(3^{6} \theta^4+2 3^{5} x\left(7\theta^2+7\theta+2\right)-2^{2} 3^{4} x^{2}\left(465\theta^4+1860\theta^3+3069\theta^2+2418\theta+752\right)-3^{3} x^{3}(\theta+2)(\theta+1)(19327\theta^2+57981\theta+52674)+2^{5} 3^{2} x^{4}(17298\theta^2+69192\theta+54655)(\theta+2)^2+2^{4} 3^{2} 11 31 251 x^{5}(\theta+1)(\theta+2)(\theta+3)(\theta+4)-2^{3} 11^{2} 251^{2} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -4/3, 196/9, -604/27, 83956/81, ... --> OEIS Normalized instanton numbers (n0=1): 2/3, 5/3, 13/3, 59/3, 119, ... ; Common denominator:...
\(-(11z-3)(22z+3)(1004z^2+66z-9)(251z^2-33z-9)\)
| \(-\frac{ 3}{ 22}\) | \(\frac{ 33}{ 502}-\frac{ 45}{ 502}\sqrt{ 5}\) | \(-\frac{ 33}{ 1004}-\frac{ 45}{ 1004}\sqrt{ 5}\) | \(0\) | \(-\frac{ 33}{ 1004}+\frac{ 45}{ 1004}\sqrt{ 5}\) | \(\frac{ 33}{ 502}+\frac{ 45}{ 502}\sqrt{ 5}\) | \(\frac{ 3}{ 11}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(4\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(5\) |
3
New Number: 7.6 | AESZ: | Superseeker: 1/3 5/3 | Hash: 24ba77c97bc4b46c39a41c77cc1d1ef4
Degree: 7
\(3^{2} \theta^4-3 x\left(112\theta^4+140\theta^3+133\theta^2+63\theta+12\right)+x^{2}\left(4393\theta^4+9340\theta^3+10903\theta^2+6360\theta+1488\right)-2 x^{3}\left(11669\theta^4+27720\theta^3+27019\theta^2+8460\theta-912\right)+2^{2} x^{4}\left(6799\theta^4-10288\theta^3-82183\theta^2-119168\theta-52672\right)+2^{3} 7 x^{5}(\theta+1)(2611\theta^3+15537\theta^2+26998\theta+14360)-2^{6} 7^{2} x^{6}(\theta+1)(\theta+2)(83\theta^2+105\theta-66)-2^{10} 7^{3} x^{7}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 28, 232, 2188, ... --> OEIS Normalized instanton numbers (n0=1): 1/3, 5/6, 5/3, 19/3, 29, ... ; Common denominator:...
\(-(2z+1)(8z-1)(7z-1)(16z-1)(z+1)(-3+14z)^2\)
| \(-1\) | \(-\frac{ 1}{ 2}\) | \(0\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 8}\) | \(\frac{ 1}{ 7}\) | \(\frac{ 3}{ 14}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(2\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(3\) |
4
New Number: 7.7 | AESZ: | Superseeker: 2/3 13/3 | Hash: c7abb9c42d46f14955f0f23351082bef
Degree: 7
\(3^{2} \theta^4-2 3 x\left(88\theta^4+110\theta^3+103\theta^2+48\theta+9\right)+2^{2} x^{2}\left(2923\theta^4+6610\theta^3+8041\theta^2+4908\theta+1206\right)-x^{3}\left(123365\theta^4+374814\theta^3+519741\theta^2+346176\theta+89676\right)+2 x^{4}\left(309657\theta^4+1102938\theta^3+1591157\theta^2+1032920\theta+249740\right)-2^{3} 11 x^{5}(\theta+1)(12897\theta^3+35469\theta^2+31181\theta+8042)-2^{3} 11^{2} x^{6}(\theta+1)(\theta+2)(355\theta^2+1047\theta+806)-2^{4} 11^{3} x^{7}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, 56, 636, 8196, ... --> OEIS Normalized instanton numbers (n0=1): 2/3, 5/3, 13/3, 59/3, 119, ... ; Common denominator:...
\(-(11z-1)(4z^2+22z-1)(z^2+11z-1)(-3+22z)^2\)
| \(-\frac{ 11}{ 2}-\frac{ 5}{ 2}\sqrt{ 5}\) | \(-\frac{ 11}{ 4}-\frac{ 5}{ 4}\sqrt{ 5}\) | \(0\) | \(-\frac{ 11}{ 4}+\frac{ 5}{ 4}\sqrt{ 5}\) | \(-\frac{ 11}{ 2}+\frac{ 5}{ 2}\sqrt{ 5}\) | \(\frac{ 1}{ 11}\) | \(\frac{ 3}{ 22}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(2\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(3\) |