1
New Number: 3.19 | AESZ: 389 | Superseeker: 66 69048 | Hash: c5cca5b7bfc61c4e8b38fab025244078
Degree: 3
\(\theta^4-2 x\left(742\theta^4+1484\theta^3+1295\theta^2+553\theta+95\right)+2^{2} 5^{3} x^{2}(\theta+1)^2(1468\theta^2+2936\theta+1211)-2^{4} 5^{6} 11^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 190, 61170, 22892500, 9212271250, ... --> OEIS Normalized instanton numbers (n0=1): 66, -1780, 69048, -3847892, 244783420, ... ; Common denominator:...
\(-(484z-1)(-1+500z)^2\)
| \(0\) | \(\frac{ 1}{ 500}\) | \(\frac{ 1}{ 484}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(0\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(2\) |
| \(0\) | \(1\) | \(2\) | \(\frac{ 5}{ 2}\) |
2
New Number: 8.1 | AESZ: 102 | Superseeker: 8 1053 | Hash: e928905653beb9d844e6a942f50d94ac
Degree: 8
\(\theta^4-x(7\theta^2+7\theta+2)(11\theta^2+11\theta+3)-x^{2}\left(1049\theta^4+4100\theta^3+5689\theta^2+3178\theta+640\right)+2^{3} x^{3}\left(77\theta^4-462\theta^3-1420\theta^2-1053\theta-252\right)+2^{4} x^{4}\left(1041\theta^4+2082\theta^3-1406\theta^2-2447\theta-746\right)+2^{6} x^{5}\left(77\theta^4+770\theta^3+428\theta^2-93\theta-80\right)-2^{6} x^{6}\left(1049\theta^4+96\theta^3-317\theta^2+96\theta+100\right)-2^{9} x^{7}(7\theta^2+7\theta+2)(11\theta^2+11\theta+3)+2^{12} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, 190, 8232, 432846, ... --> OEIS Normalized instanton numbers (n0=1): 8, 153/2, 1053, 49101/2, 670214, ... ; Common denominator:...
\((64z^2+88z-1)(z^2-11z-1)(-1+8z^2)^2\)
| \(-\frac{ 11}{ 16}-\frac{ 5}{ 16}\sqrt{ 5}\) | \(-\frac{ 1}{ 4}\sqrt{ 2}\) | \(\frac{ 11}{ 2}-\frac{ 5}{ 2}\sqrt{ 5}\) | \(0\) | \(-\frac{ 11}{ 16}+\frac{ 5}{ 16}\sqrt{ 5}\) | \(\frac{ 1}{ 4}\sqrt{ 2}\) | \(\frac{ 11}{ 2}+\frac{ 5}{ 2}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(1\) |
3
New Number: 8.61 | AESZ: | Superseeker: -32/5 -863/5 | Hash: 9699709447380eb1373469a1cf5a9586
Degree: 8
\(5^{2} \theta^4+5 x\left(351\theta^4+894\theta^3+752\theta^2+305\theta+50\right)+x^{2}\left(17519\theta^4+143132\theta^3+257359\theta^2+171910\theta+41600\right)-2^{3} x^{3}\left(29420\theta^4+38388\theta^3-153289\theta^2-215145\theta-74900\right)-2^{4} 3 x^{4}\left(21007\theta^4+218446\theta^3+428718\theta^2+312263\theta+79010\right)+2^{6} x^{5}\left(140935\theta^4+605458\theta^3+887488\theta^2+551709\theta+125368\right)-2^{6} x^{6}\left(70937\theta^4+221280\theta^3+204067\theta^2+54336\theta-3916\right)+2^{9} x^{7}\left(1182\theta^4+2556\theta^3+2095\theta^2+817\theta+142\right)-2^{12} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -10, 190, -4888, 151246, ... --> OEIS Normalized instanton numbers (n0=1): -32/5, -33/10, -863/5, 715/2, -83882/5, ... ; Common denominator:...
\(-(8z+1)(8z^3-1119z^2-75z-1)(5-32z+8z^2)^2\)
| \(-\frac{ 1}{ 8}\) | ≈\(-0.048631\) | ≈\(-0.018367\) | \(0\) | \(2-\frac{ 3}{ 4}\sqrt{ 6}\) | \(2+\frac{ 3}{ 4}\sqrt{ 6}\) | ≈\(139.941998\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(3\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(2\) | \(0\) | \(4\) | \(4\) | \(2\) | \(1\) |