1
New Number: 2.69 | AESZ: 205 | Superseeker: 1 5 | Hash: 4fb2e7002e630237d0458c3985cd6a18
Degree: 2
\(\theta^4-x\left(59\theta^4+118\theta^3+105\theta^2+46\theta+8\right)+2^{5} 3 x^{2}(\theta+1)^2(3\theta+2)(3\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 120, 2240, 46840, ... --> OEIS Normalized instanton numbers (n0=1): 1, 7/4, 5, 24, 759/5, ... ; Common denominator:...
\((32z-1)(27z-1)\)
| \(0\) | \(\frac{ 1}{ 32}\) | \(\frac{ 1}{ 27}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
| \(0\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(2\) | \(2\) | \(\frac{ 4}{ 3}\) |
2
New Number: 3.24 | AESZ: | Superseeker: -2 -108 | Hash: 3c89cc2017daa2eba88c016b8ae5865c
Degree: 3
\(\theta^4+2 x(2\theta+1)^2(3\theta^2+3\theta+1)-2^{2} x^{2}(2\theta+1)(2\theta+3)(47\theta^2+94\theta+51)+2^{4} 7 x^{3}(2\theta+1)(2\theta+3)^2(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -2, 54, -980, 26950, ... --> OEIS Normalized instanton numbers (n0=1): -2, 17, -108, 1498, -19630, ... ; Common denominator:...
\((16z-1)(112z^2-40z-1)\)
| \(\frac{ 5}{ 28}-\frac{ 1}{ 7}\sqrt{ 2}\) | \(0\) | \(\frac{ 1}{ 16}\) | \(\frac{ 5}{ 28}+\frac{ 1}{ 7}\sqrt{ 2}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(0\) | \(2\) | \(2\) | \(\frac{ 5}{ 2}\) |
3
New Number: 5.104 | AESZ: 357 | Superseeker: 7/13 21/13 | Hash: afee0651c9b3b8e98079f5c2d5bfa8a5
Degree: 5
\(13^{2} \theta^4-13 x\left(441\theta^4+690\theta^3+631\theta^2+286\theta+52\right)+2^{4} x^{2}\left(5121\theta^4+15576\theta^3+21215\theta^2+13702\theta+3445\right)-2^{10} x^{3}\left(640\theta^4+2847\theta^3+5078\theta^2+4056\theta+1196\right)+2^{14} x^{4}\left(125\theta^4+562\theta^3+905\theta^2+624\theta+157\right)-2^{21} x^{5}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 20, 112, 916, ... --> OEIS Normalized instanton numbers (n0=1): 7/13, -10/13, 21/13, 296/13, 608/13, ... ; Common denominator:...
\(-(16z-1)(128z^2-13z+1)(-13+32z)^2\)
| \(0\) | \(\frac{ 13}{ 256}-\frac{ 7}{ 256}\sqrt{ 7}I\) | \(\frac{ 13}{ 256}+\frac{ 7}{ 256}\sqrt{ 7}I\) | \(\frac{ 1}{ 16}\) | \(\frac{ 13}{ 32}\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) |
| \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(1\) |