1
New Number: 6.15 | AESZ: | Superseeker: 64 76608 | Hash: 0130ee676bad42a2e117bca3367f8cf0
Degree: 6
\(\theta^4+2^{4} x\left(56\theta^4+16\theta^3+22\theta^2+14\theta+3\right)+2^{10} x^{2}\left(308\theta^4+272\theta^3+347\theta^2+174\theta+35\right)+2^{18} x^{3}\left(212\theta^4+384\theta^3+473\theta^2+282\theta+69\right)+2^{26} x^{4}\left(77\theta^4+232\theta^3+327\theta^2+226\theta+62\right)+2^{35} x^{5}(7\theta^2+17\theta+13)(\theta+1)^2+2^{42} x^{6}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, -48, 3088, -231168, 19207440, ... --> OEIS Normalized instanton numbers (n0=1): 64, -1732, 76608, -4429212, 296488640, ... ; Common denominator:...
\((64z+1)^2(128z+1)^2(256z+1)^2\)
| \(-\frac{ 1}{ 64}\) | \(-\frac{ 1}{ 128}\) | \(-\frac{ 1}{ 256}\) | \(0\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(2\) |
| \(1\) | \(1\) | \(4\) | \(0\) | \(2\) |
2
New Number: 7.2 | AESZ: | Superseeker: -80 -249872 | Hash: 341389ebf4ab0242c5b70d9a8fd7a1d9
Degree: 7
\(\theta^4+2^{4} x\left(22\theta^4+64\theta^3+51\theta^2+19\theta+3\right)-2^{9} x^{2}\left(174\theta^4-624\theta^3-945\theta^2-417\theta-80\right)-2^{14} x^{3}\left(2230\theta^4+3000\theta^3-5121\theta^2-3813\theta-971\right)+2^{19} x^{4}\left(2860\theta^4-33320\theta^3+3363\theta^2+6847\theta+2402\right)+2^{27} x^{5}\left(7332\theta^4+480\theta^3+81\theta^2+1380\theta+719\right)+2^{36} 7 x^{6}(\theta+1)(46\theta^3+86\theta^2+67\theta+20)-2^{45} 7^{2} x^{7}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -48, 5072, -733440, 124117776, ... --> OEIS Normalized instanton numbers (n0=1): -80, -4202, -249872, -22251117, -2195810928, ... ; Common denominator:...
\(-(64z+1)(32z-1)(224z-1)^2(256z+1)^3\)
| \(-\frac{ 1}{ 64}\) | \(-\frac{ 1}{ 256}\) | \(0\) | \(\frac{ 1}{ 224}\) | \(\frac{ 1}{ 32}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(\frac{ 3}{ 2}\) | \(0\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(1\) |
3
New Number: 8.81 | AESZ: | Superseeker: -64 54464 | Hash: 3cc4cfea037192a297dc29928555ed1d
Degree: 8
\(\theta^4+2^{4} x\left(40\theta^4+56\theta^3+46\theta^2+18\theta+3\right)+2^{10} x^{2}\left(200\theta^4+296\theta^3+357\theta^2+236\theta+58\right)+2^{16} x^{3}\left(720\theta^4+888\theta^3+446\theta^2+417\theta+126\right)+2^{22} x^{4}\left(1828\theta^4+2360\theta^3+1237\theta^2-93\theta-199\right)+2^{29} x^{5}\left(1684\theta^4+1864\theta^3+2547\theta^2+865\theta+28\right)+2^{36} x^{6}\left(1124\theta^4+1416\theta^3+1715\theta^2+969\theta+221\right)+2^{43} 3 x^{7}\left(148\theta^4+344\theta^3+367\theta^2+195\theta+42\right)+2^{53} 3^{2} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -48, 4112, -470784, 65066256, ... --> OEIS Normalized instanton numbers (n0=1): -64, 2380, 54464, -1677212, -279711424, ... ; Common denominator:...
\((128z+1)(256z+1)(64z+1)^2(24576z^2+64z+1)^2\)
| \(-\frac{ 1}{ 64}\) | \(-\frac{ 1}{ 128}\) | \(-\frac{ 1}{ 256}\) | \(-\frac{ 1}{ 768}-\frac{ 1}{ 768}\sqrt{ 23}I\) | \(-\frac{ 1}{ 768}+\frac{ 1}{ 768}\sqrt{ 23}I\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(3\) | \(3\) | \(0\) | \(1\) |
| \(1\) | \(2\) | \(2\) | \(4\) | \(4\) | \(0\) | \(1\) |