1
New Number: 2.68 | AESZ: 406 | Superseeker: -12 -1668 | Hash: d3a5c69671a7189e15cf1394437380a2
Degree: 2
\(\theta^4-2^{2} x\left(128\theta^4+224\theta^3+197\theta^2+85\theta+14\right)+2^{7} x^{2}(2\theta+1)(4\theta+5)(8\theta+5)(8\theta+9)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 56, 7272, 1200000, 222009000, ... --> OEIS Normalized instanton numbers (n0=1): -12, -186, -1668, -25974, -243552, ... ; Common denominator:...
\((256z-1)^2\)
| \(0\) | \(\frac{ 1}{ 256}\) | \(\infty\) |
|---|---|---|
| \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(\frac{ 1}{ 4}\) | \(\frac{ 5}{ 8}\) |
| \(0\) | \(1\) | \(\frac{ 9}{ 8}\) |
| \(0\) | \(\frac{ 5}{ 4}\) | \(\frac{ 5}{ 4}\) |
2
New Number: 10.9 | AESZ: | Superseeker: 4 116 | Hash: dbcf215f85612454543d472ffd3bffa9
Degree: 10
\(\theta^4-2^{2} x\left(38\theta^4+70\theta^3+93\theta^2+58\theta+14\right)+2^{4} x^{2}\left(609\theta^4+2214\theta^3+4255\theta^2+4118\theta+1630\right)-2^{8} x^{3}\left(1357\theta^4+7284\theta^3+18055\theta^2+22233\theta+11143\right)+2^{10} x^{4}\left(7450\theta^4+52316\theta^3+157665\theta^2+230387\theta+134924\right)-2^{14} x^{5}\left(6580\theta^4+56446\theta^3+198857\theta^2+332342\theta+219249\right)+2^{16} x^{6}\left(15153\theta^4+151710\theta^3+606095\theta^2+1128594\theta+818733\right)-2^{20} x^{7}\left(5621\theta^4+63496\theta^3+280382\theta^2+568755\theta+444393\right)+2^{22} x^{8}\left(5152\theta^4+63904\theta^3+304853\theta^2+659693\theta+544236\right)-2^{26} 3 x^{9}\left(220\theta^4+2928\theta^3+14781\theta^2+33462\theta+28605\right)+2^{28} 3^{2} x^{10}\left((2\theta+7)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 56, 2192, 74112, 2319376, ... --> OEIS Normalized instanton numbers (n0=1): 4, 31/2, 116, 2477/2, 16876, ... ; Common denominator:...
\((1-48z+256z^2)(4z-1)^2(24z-1)^2(8z-1)^2(16z-1)^2\)
| \(0\) | \(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 24}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 8}\) | \(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 7}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(0\) | \(0\) | \(1\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(0\) | \(1\) | \(-2\) | \(1\) | \(1\) | \(1\) | \(3\) | \(\frac{ 7}{ 2}\) |
| \(0\) | \(2\) | \(3\) | \(1\) | \(1\) | \(2\) | \(4\) | \(\frac{ 7}{ 2}\) |
3
New Number: 7.7 | AESZ: | Superseeker: 2/3 13/3 | Hash: c7abb9c42d46f14955f0f23351082bef
Degree: 7
\(3^{2} \theta^4-2 3 x\left(88\theta^4+110\theta^3+103\theta^2+48\theta+9\right)+2^{2} x^{2}\left(2923\theta^4+6610\theta^3+8041\theta^2+4908\theta+1206\right)-x^{3}\left(123365\theta^4+374814\theta^3+519741\theta^2+346176\theta+89676\right)+2 x^{4}\left(309657\theta^4+1102938\theta^3+1591157\theta^2+1032920\theta+249740\right)-2^{3} 11 x^{5}(\theta+1)(12897\theta^3+35469\theta^2+31181\theta+8042)-2^{3} 11^{2} x^{6}(\theta+1)(\theta+2)(355\theta^2+1047\theta+806)-2^{4} 11^{3} x^{7}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, 56, 636, 8196, ... --> OEIS Normalized instanton numbers (n0=1): 2/3, 5/3, 13/3, 59/3, 119, ... ; Common denominator:...
\(-(11z-1)(4z^2+22z-1)(z^2+11z-1)(-3+22z)^2\)
| \(-\frac{ 11}{ 2}-\frac{ 5}{ 2}\sqrt{ 5}\) | \(-\frac{ 11}{ 4}-\frac{ 5}{ 4}\sqrt{ 5}\) | \(0\) | \(-\frac{ 11}{ 4}+\frac{ 5}{ 4}\sqrt{ 5}\) | \(-\frac{ 11}{ 2}+\frac{ 5}{ 2}\sqrt{ 5}\) | \(\frac{ 1}{ 11}\) | \(\frac{ 3}{ 22}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(2\) |
| \(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(3\) |