1
New Number: 4.43 | AESZ: 225 | Superseeker: 93984 25265152551072 | Hash: 5993002ccf811247be9232b089dd8e3a
Degree: 4
\(\theta^4+2^{4} x\left(22192\theta^4-17056\theta^3-9576\theta^2-1048\theta-49\right)+2^{20} x^{2}\left(33648\theta^4-44688\theta^3+16224\theta^2+1764\theta+17\right)+2^{34} 5 x^{3}\left(6512\theta^4-6144\theta^3-4440\theta^2-1536\theta-193\right)-2^{55} 5^{2} x^{4}\left((2\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 784, 3226896, 20413907200, 157477179235600, ... --> OEIS Normalized instanton numbers (n0=1): 93984, -1084521600, 25265152551072, -787700706860008320, 28889437619654310485088, ... ; Common denominator:...
\(-(536870912z^2-27392z-1)(1+163840z)^2\)
| ≈\(-2.5e-05\) | \(-\frac{ 1}{ 163840}\) | \(0\) | \(s_2\) | \(s_1\) | ≈\(7.6e-05\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(3\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(2\) | \(4\) | \(0\) | \(2\) | \(2\) | \(2\) | \(\frac{ 1}{ 2}\) |
2
New Number: 8.18 | AESZ: 197 | Superseeker: 3 1621/13 | Hash: 4cc8bdba73e5fa6cb4089fa5296429de
Degree: 8
\(13^{2} \theta^4-13^{2} x\left(41\theta^4+82\theta^3+67\theta^2+26\theta+4\right)-2^{3} 13 x^{2}\left(471\theta^4+1788\theta^3+2555\theta^2+1534\theta+338\right)+2^{6} 13 x^{3}\left(251\theta^4+1014\theta^3+1798\theta^2+1413\theta+405\right)+2^{9} x^{4}\left(749\theta^4+436\theta^3-4908\theta^2-6266\theta-2145\right)-2^{12} x^{5}\left(379\theta^4+1270\theta^3+967\theta^2-42\theta-178\right)-2^{15} x^{6}\left(9\theta^4-156\theta^3-273\theta^2-156\theta-28\right)+2^{18} x^{7}\left(13\theta^4+26\theta^3+20\theta^2+7\theta+1\right)-2^{21} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 68, 1552, 43156, ... --> OEIS Normalized instanton numbers (n0=1): 3, 226/13, 1621/13, 20666/13, 289056/13, ... ; Common denominator:...
\(-(z-1)(8z+1)(64z^2-48z+1)(-13+64z^2)^2\)
| \(-\frac{ 1}{ 8}\sqrt{ 13}\) | \(-\frac{ 1}{ 8}\) | \(0\) | \(\frac{ 3}{ 8}-\frac{ 1}{ 4}\sqrt{ 2}\) | \(\frac{ 1}{ 8}\sqrt{ 13}\) | \(\frac{ 3}{ 8}+\frac{ 1}{ 4}\sqrt{ 2}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(2\) | \(1\) |
3
New Number: 8.28 | AESZ: 303 | Superseeker: 151/13 26293/13 | Hash: e081c85684dd16a72eeaf5a1b139b912
Degree: 8
\(13^{2} \theta^4-13 x\left(1505\theta^4+2746\theta^3+2127\theta^2+754\theta+104\right)+2^{2} x^{2}\left(22961\theta^4-2086\theta^3-55741\theta^2-41574\theta-9256\right)+2^{5} x^{3}\left(7524\theta^4+28098\theta^3+16131\theta^2+2691\theta-52\right)-2^{7} x^{4}\left(7241\theta^4+6214\theta^3+17522\theta^2+15423\theta+4146\right)-2^{8} x^{5}\left(6087\theta^4+1806\theta^3-3905\theta^2-3796\theta-1036\right)+2^{10} x^{6}\left(553\theta^4+4062\theta^3+4405\theta^2+1752\theta+220\right)+2^{14} x^{7}\left(82\theta^4+230\theta^3+275\theta^2+160\theta+37\right)+2^{18} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 292, 15776, 1030036, ... --> OEIS Normalized instanton numbers (n0=1): 151/13, 1436/13, 26293/13, 719465/13, 24184128/13, ... ; Common denominator:...
\((z-1)(64z^3+304z^2+108z-1)(-13+44z+64z^2)^2\)
| ≈\(-4.362346\) | \(-\frac{ 11}{ 32}-\frac{ 1}{ 32}\sqrt{ 329}\) | ≈\(-0.396684\) | \(0\) | ≈\(0.009029\) | \(-\frac{ 11}{ 32}+\frac{ 1}{ 32}\sqrt{ 329}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(1\) |