1
New Number: 6.41 | AESZ: | Superseeker: 161/13 26946/13 | Hash: a18253e410f284ecdac465808ec8a6e1
Degree: 6
\(13^{6} \theta^4-13^{5} x\left(1382\theta^4+2764\theta^3+2109\theta^2+727\theta+96\right)-13^{4} x^{2}\left(104743\theta^4+418972\theta^3+637899\theta^2+437854\theta+116928\right)-2^{2} 13^{3} x^{3}\left(746084\theta^4+4476504\theta^3+9750459\theta^2+9107109\theta+3146850\right)-2^{5} 7 13^{2} x^{4}\left(180214\theta^4+1441712\theta^3+4063657\theta^2+4720932\theta+1930533\right)-2^{9} 3 5 7^{2} 13 x^{5}(\theta+4)(\theta+1)(688\theta^2+3440\theta+3823)-2^{13} 3^{2} 5^{2} 7^{3} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 96/13, 49776/169, 35502696/2197, 30531314880/28561, ... --> OEIS Normalized instanton numbers (n0=1): 161/13, 1406/13, 26946/13, 742982/13, 25168759/13, ... ; Common denominator:...
\(-(-169+18720z+22400z^2)(8z+13)^2(21z+13)^2\)
| \(0\) | \(\infty\) | \(-\frac{ 13}{ 21}\) | \(-\frac{ 117}{ 280}-\frac{ 169}{ 560}\sqrt{ 2}\) | \(-\frac{ 13}{ 8}\) | \(-\frac{ 117}{ 280}+\frac{ 169}{ 560}\sqrt{ 2}\) |
|---|---|---|---|---|---|
| \(0\) | \(1\) | \(0\) | \(0\) | \(0\) | \(0\) |
| \(0\) | \(2\) | \(0\) | \(1\) | \(0\) | \(1\) |
| \(0\) | \(4\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(5\) | \(1\) | \(2\) | \(1\) | \(2\) |
2
New Number: 8.73 | AESZ: | Superseeker: 161/13 26946/13 | Hash: 13db5d8c98a3d4f31589970217896191
Degree: 8
\(13^{2} \theta^4-13 x\theta(614\theta^3+1804\theta^2+1149\theta+247)-x^{2}\left(775399\theta^4+2692636\theta^3+3693483\theta^2+2450110\theta+648960\right)-2^{2} x^{3}\left(5408420\theta^4+24616488\theta^3+45163287\theta^2+38795913\theta+12838410\right)-2^{5} x^{4}\left(9763642\theta^4+55386224\theta^3+123097843\theta^2+124066416\theta+46600563\right)-2^{9} 3 x^{5}(\theta+1)(1717504\theta^3+9940776\theta^2+20063523\theta+13933966)-2^{13} 3^{2} x^{6}(\theta+1)(\theta+2)(178975\theta^2+874119\theta+1112486)-2^{19} 3^{4} x^{7}(\theta+3)(\theta+2)(\theta+1)(857\theta+2533)-2^{23} 3^{6} 7 x^{8}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 240, 10440, 679104, ... --> OEIS Normalized instanton numbers (n0=1): 161/13, 1406/13, 26946/13, 742982/13, 25168759/13, ... ; Common denominator:...
\(-(-1+96z+896z^2)(9z+1)^2(96z+13)^2(8z+1)^2\)
| \(0\) | \(-\frac{ 3}{ 56}-\frac{ 5}{ 112}\sqrt{ 2}\) | \(\infty\) | \(-\frac{ 13}{ 96}\) | \(-\frac{ 3}{ 56}+\frac{ 5}{ 112}\sqrt{ 2}\) | \(-\frac{ 1}{ 9}\) | \(-\frac{ 1}{ 8}\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(1\) | \(0\) | \(0\) | \(0\) | \(0\) |
| \(0\) | \(1\) | \(2\) | \(1\) | \(1\) | \(0\) | \(0\) |
| \(0\) | \(1\) | \(3\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(2\) | \(4\) | \(4\) | \(2\) | \(1\) | \(1\) |