1
New Number: 5.67 | AESZ: 275 | Superseeker: 116/5 186172/5 | Hash: f411d346afd4b8ff14b8b4c1836bae77
Degree: 5
\(5^{2} \theta^4-2^{2} 5 x\left(592\theta^4+1568\theta^3+1419\theta^2+635\theta+115\right)+2^{4} x^{2}\left(65536\theta^4+514048\theta^3+902816\theta^2+598400\theta+144735\right)+2^{10} x^{3}\left(106496\theta^4+122880\theta^3-594816\theta^2-794880\theta-265065\right)-2^{19} x^{4}\left(8192\theta^4+77824\theta^3+145728\theta^2+102016\theta+24527\right)-2^{26} x^{5}(8\theta+5)(8\theta+7)(8\theta+9)(8\theta+11)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 92, 14124, 2572400, 510577900, ... --> OEIS Normalized instanton numbers (n0=1): 116/5, -5993/5, 186172/5, -8039756/5, 384321296/5, ... ; Common denominator:...
\(-(-1+64z)(256z+5)^2(256z-1)^2\)
| \(-\frac{ 5}{ 256}\) | \(0\) | \(\frac{ 1}{ 256}\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 5}{ 8}\) |
| \(1\) | \(0\) | \(0\) | \(1\) | \(\frac{ 7}{ 8}\) |
| \(3\) | \(0\) | \(1\) | \(1\) | \(\frac{ 9}{ 8}\) |
| \(4\) | \(0\) | \(1\) | \(2\) | \(\frac{ 11}{ 8}\) |
2
New Number: 11.9 | AESZ: | Superseeker: 17/3 4127/9 | Hash: fa7c260e6f07cef5d727e6af380a6373
Degree: 11
\(3^{2} \theta^4-3 x\theta(20\theta^3+196\theta^2+125\theta+27)-x^{2}\left(19127\theta^4+69044\theta^3+89705\theta^2+54504\theta+13248\right)-2 x^{3}\left(285799\theta^4+1251420\theta^3+2142633\theta^2+1678248\theta+511560\right)-2^{2} x^{4}\left(2058125\theta^4+11190220\theta^3+23374875\theta^2+21658060\theta+7556504\right)-2^{3} x^{5}\left(8570685\theta^4+57030456\theta^3+140934413\theta^2+149627146\theta+57858760\right)-2^{6} x^{6}\left(5382486\theta^4+43183593\theta^3+124360784\theta^2+148979343\theta+62839586\right)-2^{7} x^{7}\left(7897671\theta^4+75745098\theta^3+252663545\theta^2+339244430\theta+154810568\right)-2^{10} x^{8}(\theta+1)(1454893\theta^3+15409953\theta^2+50286726\theta+48898444)-2^{11} x^{9}(\theta+1)(\theta+2)(227963\theta^2+3375435\theta+10342960)+2^{14} x^{10}(\theta+3)(\theta+2)(\theta+1)(48476\theta+271867)-2^{15} 3 5 13 23 x^{11}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 92, 2328, 91212, ... --> OEIS Normalized instanton numbers (n0=1): 17/3, 257/6, 4127/9, 23827/3, 496999/3, ... ; Common denominator:...
\(-(5z+1)(13z+1)(6z+1)(368z^2+56z-1)(4z+1)^2(8z^2-26z-3)^2\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 5}\) | \(-\frac{ 7}{ 92}-\frac{ 3}{ 46}\sqrt{ 2}\) | \(-\frac{ 1}{ 6}\) | \(\frac{ 13}{ 8}-\frac{ 1}{ 8}\sqrt{ 193}\) | \(-\frac{ 1}{ 13}\) | \(0\) | \(-\frac{ 7}{ 92}+\frac{ 3}{ 46}\sqrt{ 2}\) | \(\frac{ 13}{ 8}+\frac{ 1}{ 8}\sqrt{ 193}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(3\) |
| \(1\) | \(2\) | \(2\) | \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(4\) |
3
New Number: 8.65 | AESZ: | Superseeker: -24/5 -1608/5 | Hash: 5e457fa5807a784e24220c973aeceba8
Degree: 8
\(5^{2} \theta^4+2^{2} 5 x\left(73\theta^4+122\theta^3+96\theta^2+35\theta+5\right)-2^{4} x^{2}\left(134\theta^4+2072\theta^3+3924\theta^2+2660\theta+645\right)-2^{6} x^{3}\left(708\theta^4+672\theta^3-2898\theta^2-3750\theta-1285\right)+2^{10} x^{4}\left(110\theta^4+700\theta^3+498\theta^2-56\theta-105\right)+2^{12} x^{5}\left(61\theta^4-266\theta^3-544\theta^2-373\theta-88\right)-2^{14} x^{6}\left(86\theta^4+168\theta^3+172\theta^2+108\theta+31\right)+2^{16} x^{7}\left(32\theta^4+112\theta^3+158\theta^2+102\theta+25\right)-2^{20} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -4, 92, -2704, 95596, ... --> OEIS Normalized instanton numbers (n0=1): -24/5, 329/10, -1608/5, 48409/10, -455264/5, ... ; Common denominator:...
\(-(4z-1)(256z^3-192z^2+56z+1)(-5-16z+32z^2)^2\)
| \(\frac{ 1}{ 4}-\frac{ 1}{ 8}\sqrt{ 14}\) | ≈\(-0.016861\) | \(0\) | \(\frac{ 1}{ 4}\) | ≈\(0.38343-0.290965I\) | ≈\(0.38343+0.290965I\) | \(\frac{ 1}{ 4}+\frac{ 1}{ 8}\sqrt{ 14}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(3\) | \(1\) |
| \(4\) | \(2\) | \(0\) | \(2\) | \(2\) | \(2\) | \(4\) | \(1\) |