1
New Number: 5.43 | AESZ: 234 | Superseeker: 18/7 5676/7 | Hash: 3e70b30959c0c3bd799b435b9c842186
Degree: 5
\(7^{2} \theta^4-2 7 x\theta(192\theta^3+60\theta^2+37\theta+7)-2^{2} x^{2}\left(17608\theta^4+115144\theta^3+166715\theta^2+94556\theta+18816\right)+2^{4} 3^{2} x^{3}\left(20288\theta^4+57288\theta^3+27524\theta^2-7455\theta-5026\right)-2^{6} 3^{5} x^{4}(2\theta+1)(458\theta^3-657\theta^2-1799\theta-846)-2^{12} 3^{8} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 96, 1440, 90720, ... --> OEIS Normalized instanton numbers (n0=1): 18/7, 515/7, 5676/7, 133796/7, 2929726/7, ... ; Common denominator:...
\(-(64z-1)(36z+1)(4z+1)(-7+108z)^2\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 36}\) | \(0\) | \(\frac{ 1}{ 64}\) | \(\frac{ 7}{ 108}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(\frac{ 3}{ 2}\) |
2
New Number: 8.35 | AESZ: 326 | Superseeker: 11/13 385/39 | Hash: 946b91838924db64fe0ebdf0d473e621
Degree: 8
\(13^{2} \theta^4-13 x\theta(56\theta^3+178\theta^2+115\theta+26)-x^{2}\left(28466\theta^4+109442\theta^3+165603\theta^2+117338\theta+32448\right)-x^{3}\left(233114\theta^4+1257906\theta^3+2622815\theta^2+2467842\theta+872352\right)-x^{4}\left(989585\theta^4+6852298\theta^3+17737939\theta^2+19969754\theta+8108448\right)-x^{5}(\theta+1)(2458967\theta^3+18007287\theta^2+44047582\theta+35386584)-3^{2} x^{6}(\theta+1)(\theta+2)(393163\theta^2+2539029\theta+4164444)-3^{3} 11 x^{7}(\theta+3)(\theta+2)(\theta+1)(8683\theta+34604)-3^{3} 11^{2} 13 17 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 12, 96, 1116, ... --> OEIS Normalized instanton numbers (n0=1): 11/13, 30/13, 385/39, 672/13, 4437/13, ... ; Common denominator:...
\(-(3z+1)(13z^2+5z+1)(153z^3+75z^2+14z-1)(13+11z)^2\)
| \(-\frac{ 13}{ 11}\) | \(-\frac{ 1}{ 3}\) | ≈\(-0.272124-0.216493I\) | ≈\(-0.272124+0.216493I\) | \(-\frac{ 5}{ 26}-\frac{ 3}{ 26}\sqrt{ 3}I\) | \(-\frac{ 5}{ 26}+\frac{ 3}{ 26}\sqrt{ 3}I\) | \(0\) | ≈\(0.054052\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) |
3
New Number: 8.36 | AESZ: 327 | Superseeker: 24/29 284/29 | Hash: 586c1906112cbba9b2d54c57ce2add99
Degree: 8
\(29^{2} \theta^4+2 29 x\theta(24\theta^3-198\theta^2-128\theta-29)-2^{2} x^{2}\left(44284\theta^4+172954\theta^3+248589\theta^2+172057\theta+47096\right)-2^{2} x^{3}\left(525708\theta^4+2414772\theta^3+4447643\theta^2+3839049\theta+1275594\right)-2^{3} x^{4}\left(1415624\theta^4+7911004\theta^3+17395449\theta^2+17396359\theta+6496262\right)-2^{4} x^{5}(\theta+1)(2152040\theta^3+12186636\theta^2+24179373\theta+16560506)-2^{5} x^{6}(\theta+1)(\theta+2)(1912256\theta^2+9108540\theta+11349571)-2^{8} 41 x^{7}(\theta+3)(\theta+2)(\theta+1)(5671\theta+16301)-2^{8} 3 19 41^{2} x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 14, 96, 1266, ... --> OEIS Normalized instanton numbers (n0=1): 24/29, 72/29, 284/29, 1616/29, 10632/29, ... ; Common denominator:...
\(-(6z+1)(152z^3+84z^2+14z-1)(2z+1)^2(82z+29)^2\)
| \(-\frac{ 1}{ 2}\) | \(-\frac{ 29}{ 82}\) | ≈\(-0.302804-0.180271I\) | ≈\(-0.302804+0.180271I\) | \(-\frac{ 1}{ 6}\) | \(0\) | ≈\(0.052976\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) |
| \(1\) | \(4\) | \(2\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) |