1
New Number: 3.16 | AESZ: 386 | Superseeker: 10 18328 | Hash: 7d032616d3bd41272e22a4d23747d7a0
Degree: 3
\(\theta^4-2 x\left(422\theta^4+844\theta^3+751\theta^2+329\theta+57\right)+2^{2} 3^{4} x^{2}(\theta+1)^2(716\theta^2+1432\theta+579)-2^{4} 3^{8} 7^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 114, 22518, 5236980, 1321024950, ... --> OEIS Normalized instanton numbers (n0=1): 10, -872, 18328, -432528, 13706388, ... ; Common denominator:...
\(-(196z-1)(-1+324z)^2\)
| \(0\) | \(\frac{ 1}{ 324}\) | \(\frac{ 1}{ 196}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(0\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(2\) |
| \(0\) | \(1\) | \(2\) | \(\frac{ 5}{ 2}\) |
2
New Number: 4.31 | AESZ: | Superseeker: -10 -340 | Hash: dc534a2a8e7bca49a87c29d9ed4e3ae8
Degree: 4
\(\theta^4-2 x\left(172\theta^4+344\theta^3+421\theta^2+249\theta+57\right)+2^{2} x^{2}\left(10852\theta^4+43408\theta^3+78043\theta^2+69270\theta+24987\right)-2^{4} 3 x^{3}\left(49536\theta^4+297216\theta^3+712240\theta^2+799248\theta+349521\right)+2^{14} 3^{2} x^{4}(3\theta+5)(3\theta+7)(6\theta+11)(6\theta+13)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 114, 11466, 1123804, 109952106, ... --> OEIS Normalized instanton numbers (n0=1): -10, -40, -340, -5820, -114610, ... ; Common denominator:...
\((108z-1)^2(64z-1)^2\)
| \(0\) | \(\frac{ 1}{ 108}\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 5}{ 3}\) |
| \(0\) | \(-\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 11}{ 6}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 13}{ 6}\) |
| \(0\) | \(\frac{ 3}{ 2}\) | \(\frac{ 3}{ 2}\) | \(\frac{ 7}{ 3}\) |
3
New Number: 11.6 | AESZ: | Superseeker: 95/102 1421/102 | Hash: e79a3108441c74cdc23a53a603a6181e
Degree: 11
\(2^{2} 3^{2} 17^{2} \theta^4-2 3 17 x\theta(116\theta^3+1414\theta^2+911\theta+204)-x^{2}\left(2596259\theta^4+9892670\theta^3+14508941\theta^2+9947652\theta+2663424\right)-3 x^{3}\left(8561767\theta^4+41744696\theta^3+79668236\theta^2+68977704\theta+22655832\right)-2^{2} x^{4}\left(28089475\theta^4+171762758\theta^3+396877187\theta^2+402013525\theta+149622901\right)-2 x^{5}\left(127339346\theta^4+963856934\theta^3+2636877099\theta^2+3042828449\theta+1247694978\right)-x^{6}\left(283337071\theta^4+2758627602\theta^3+9101625228\theta^2+11995897911\theta+5385015134\right)-2 x^{7}\left(43252385\theta^4+777895672\theta^3+3537873325\theta^2+5604936458\theta+2806067360\right)+2^{2} 3 x^{8}(\theta+1)(7613560\theta^3+27844427\theta^2-51849552\theta-134696600)+x^{9}(\theta+1)(\theta+2)(60585089\theta^2+495871401\theta+595115780)-2^{3} 3 5^{2} x^{10}(\theta+3)(\theta+2)(\theta+1)(10279\theta-113205)-2^{4} 5^{4} 7 97 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 16, 114, 1680, ... --> OEIS Normalized instanton numbers (n0=1): 95/102, 58/17, 1421/102, 1451/17, 31474/51, ... ; Common denominator:...
\(-(-1+7z+219z^2+1115z^3+1934z^4+679z^5)(z+1)^2(100z^2-197z-102)^2\)
| \(-1\) | \(\frac{ 197}{ 200}-\frac{ 1}{ 200}\sqrt{ 79609}\) | \(0\) | \(\frac{ 197}{ 200}+\frac{ 1}{ 200}\sqrt{ 79609}\) | \(#ND+#NDI\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(\frac{ 1}{ 3}\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(\frac{ 2}{ 3}\) | \(3\) | \(0\) | \(3\) | \(1\) | \(3\) |
| \(1\) | \(4\) | \(0\) | \(4\) | \(2\) | \(4\) |