1
New Number: 5.80 | AESZ: 311 | Superseeker: 25/13 875/13 | Hash: 8219f3f4bd56f6c2b2cc3ab9093b65d1
Degree: 5
\(13^{2} \theta^4-13 x\left(327\theta^4+1038\theta^3+857\theta^2+338\theta+52\right)-2^{4} x^{2}\left(12848\theta^4+42008\theta^3+52082\theta^2+28548\theta+5707\right)-2^{11} x^{3}\left(122\theta^4-1872\theta^3-6341\theta^2-5772\theta-1547\right)+2^{16} x^{4}(2\theta+1)(76\theta^3+426\theta^2+570\theta+227)+2^{23} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 84, 1840, 56980, ... --> OEIS Normalized instanton numbers (n0=1): 25/13, 1359/52, 875/13, 36572/13, 256800/13, ... ; Common denominator:...
\((8192z^3-896z^2-35z+1)(13+64z)^2\)
\(-\frac{ 13}{ 64}\) | ≈\(-0.045147\) | \(0\) | ≈\(0.020117\) | ≈\(0.134405\) | \(\infty\) |
---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
\(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
\(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(\frac{ 3}{ 2}\) |
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:...
\((z-1)(64z^3+304z^2+108z-1)(-13+44z+64z^2)^2\)
≈\(-4.362346\) | \(-\frac{ 11}{ 32}-\frac{ 1}{ 32}\sqrt{ 329}\) | ≈\(-0.396684\) | \(0\) | ≈\(0.009029\) | \(-\frac{ 11}{ 32}+\frac{ 1}{ 32}\sqrt{ 329}\) | \(1\) | \(\infty\) |
---|---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
\(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) |
\(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(1\) |