1
New Number: 13.15 | AESZ: | Superseeker: 6 626/3 | Hash: 3e24fdfe8119ac950ce846460f109e44
Degree: 13
\(\theta^4-2 x\left(16\theta^4+50\theta^3+39\theta^2+14\theta+2\right)-2^{2} x^{2}\left(219\theta^4+390\theta^3+335\theta^2+214\theta+62\right)-2^{4} x^{3}\left(115\theta^4+1068\theta^3+2660\theta^2+2022\theta+582\right)+2^{6} x^{4}\left(122\theta^4-788\theta^3+151\theta^2-913\theta-696\right)-2^{8} 3 x^{5}\left(303\theta^4-1488\theta^3-2955\theta^2-2550\theta-827\right)-2^{10} 3 x^{6}\left(37\theta^4+714\theta^3-5760\theta^2-8319\theta-3550\right)-2^{13} 3 x^{7}\left(101\theta^4+82\theta^3+102\theta^2-1679\theta-1322\right)+2^{15} 3 x^{8}\left(48\theta^4+948\theta^3-461\theta^2-1447\theta-628\right)-2^{17} x^{9}\left(89\theta^4-4392\theta^3-6123\theta^2-450\theta+1902\right)-2^{20} x^{10}\left(121\theta^4-532\theta^3-3072\theta^2-3697\theta-1348\right)+2^{23} 5 x^{11}(\theta+1)(21\theta^3+63\theta^2+206\theta+218)+2^{25} 5^{2} x^{12}(\theta+2)(\theta+1)(2\theta^2-12\theta-27)+2^{27} 5^{3} x^{13}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 4, 76, 1936, 57820, ... --> OEIS Normalized instanton numbers (n0=1): 6, 41/4, 626/3, 12349/8, 33062, ... ; Common denominator:...
\((4z-1)(4z+1)(16z^2+4z+1)(640z^3+96z^2+48z-1)(1+6z-48z^2+320z^3)^2\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 8}-\frac{ 1}{ 8}\sqrt{ 3}I\) | \(-\frac{ 1}{ 8}+\frac{ 1}{ 8}\sqrt{ 3}I\) | ≈\(-0.084967-0.266773I\) | ≈\(-0.084967+0.266773I\) | ≈\(-0.082432\) | \(0\) | ≈\(0.019933\) | ≈\(0.116216-0.156217I\) | ≈\(0.116216+0.156217I\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) | \(3\) | \(1\) | \(2\) |
| \(2\) | \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) | \(4\) | \(2\) | \(3\) |
2
New Number: 18.2 | AESZ: | Superseeker: 6 626/3 | Hash: 55d34e33f80959a1cc22d89896602d12
Degree: 18
\(5^{36} \theta^4-2 5^{34} x\left(1062\theta^4+2334\theta^3+2431\theta^2+1264\theta+270\right)+2^{2} 5^{32} x^{2}\left(320093\theta^4+1596302\theta^3+3123745\theta^2+2942536\theta+1113630\right)-2^{4} 3 5^{30} x^{3}\left(6019044\theta^4+66147274\theta^3+199338689\theta^2+265716324\theta+140408820\right)-2^{6} 3 5^{29} x^{4}\left(21064589\theta^4-712686408\theta^3-3721395346\theta^2-6814704050\theta-4678647990\right)+2^{8} 3^{2} 5^{26} x^{5}\left(11975992794\theta^4+4988365790\theta^3-283865124355\theta^2-820252227200\theta-742428845375\right)-2^{10} 3^{2} 5^{24} x^{6}\left(751496765979\theta^4+5038722749418\theta^3+527774451452\theta^2-28210592089487\theta-40377165728685\right)+2^{12} 3^{4} 5^{22} x^{7}\left(2053839509132\theta^4+38726412983468\theta^3+100208705321045\theta^2+47075279827199\theta-94563567299555\right)+2^{15} 3^{3} 5^{20} x^{8}\left(74215848255703\theta^4-1839607623231932\theta^3-9356900275220062\theta^2-15606787340081617\theta-6586759478866260\right)-2^{16} 3^{4} 5^{19} x^{9}\left(1339553061158952\theta^4-346103919288724\theta^3-32183930062302533\theta^2-95644350146690865\theta-81488332660776420\right)+2^{18} 3^{4} 5^{16} x^{10}\left(324968843289985253\theta^4+1744047067693857210\theta^3+1715197129786435655\theta^2-6334532044956661400\theta-11513434792675853625\right)-2^{20} 3^{5} 5^{14} x^{11}\left(3460747049021132226\theta^4+31298336392269716602\theta^3+104978931469185513088\theta^2+140017817259283451897\theta+43613982781047056885\right)+2^{22} 3^{5} 5^{12} x^{12}\left(80350576998319299087\theta^4+976180200725417657808\theta^3+4579453875869380552810\theta^2+9705595934827681526144\theta+7732240714165421579820\right)-2^{24} 3^{6} 5^{10} x^{13}\left(458458033401826426866\theta^4+6886135463408824297206\theta^3+39806281802402968612276\theta^2+104618897609209760830741\theta+105167289421805219654955\right)+2^{26} 3^{7} 5^{9} x^{14}\left(367293230407611531891\theta^4+6543982621478903177718\theta^3+44412685133916057233996\theta^2+135976752518751744187635\theta+158331213388111123371340\right)-2^{29} 3^{9} 5^{6} x^{15}(\theta+5)(694133174853729835197\theta^3+11024532762694581883575\theta^2+58689640052713706224130\theta+104903464776686639708350)-2^{32} 3^{11} 5^{4} 7 x^{16}(\theta+5)(\theta+6)(5759026685592741133\theta^2+12188432611308644783\theta-75995642240452623249)+2^{35} 3^{13} 5^{2} 7^{2} 31 163 277 x^{17}(\theta+5)(\theta+6)(\theta+7)(3303544726261\theta+19442784399486)-2^{40} 3^{15} 7^{3} 17 31^{2} 163^{2} 277^{2} 2273 x^{18}(\theta+5)(\theta+6)(\theta+7)(\theta+8)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 108/5, 43692/125, 20111184/3125, 12183126444/78125, ... --> OEIS Normalized instanton numbers (n0=1): 6, 41/4, 626/3, 12349/8, 33062, ... ; Common denominator:...
\(-(32z+25)(68z-25)(11783232z^3-2926800z^2+877500z-15625)(7824z^2-900z+625)^2(7419168z^3-913200z^2-33750z+15625)^2(168z-25)^3\)
No data for singularities