1
New Number: 2.56 | AESZ: 185 | Superseeker: 6 608 | Hash: 80506439e4d4fdc41f5b16e246a69fbf
Degree: 2
\(\theta^4-2 3 x(2\theta+1)^2(3\theta^2+3\theta+1)-2^{2} 3^{3} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, 162, 6180, 284130, ... --> OEIS Normalized instanton numbers (n0=1): 6, 93/2, 608, 11754, 275352, ... ; Common denominator:...
\(1-72z-432z^2\)
| \(-\frac{ 1}{ 12}-\frac{ 1}{ 18}\sqrt{ 3}\) | \(0\) | \(-\frac{ 1}{ 12}+\frac{ 1}{ 18}\sqrt{ 3}\) | \(\infty\) |
|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(0\) | \(1\) | \(1\) |
| \(2\) | \(0\) | \(2\) | \(\frac{ 3}{ 2}\) |
2
New Number: 4.75 | AESZ: | Superseeker: 6 389 | Hash: 1e24ac15c33e7bc66a4211a6f86ad179
Degree: 4
\(\theta^4+3 x\left(90\theta^4+150\theta^3+144\theta^2+69\theta+13\right)+3 x^{2}(3\theta+2)(3039\theta^3+8104\theta^2+9017\theta+3783)+3^{3} 13^{2} x^{3}(3\theta+2)(3\theta+5)(30\theta^2+80\theta+63)+3^{2} 13^{4} x^{4}(3\theta+2)(3\theta+5)^2(3\theta+8)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -39, 1989, -110604, 6425757, ... --> OEIS Normalized instanton numbers (n0=1): 6, 33, 389, 6393, 128769, ... ; Common denominator:...
\((1+135z+4563z^2)^2\)
| \(-\frac{ 5}{ 338}-\frac{ 1}{ 3042}\sqrt{ 3}I\) | \(-\frac{ 5}{ 338}+\frac{ 1}{ 3042}\sqrt{ 3}I\) | \(0\) | \(s_1\) | \(s_2\) | \(\infty\) |
|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
| \(\frac{ 1}{ 3}\) | \(\frac{ 1}{ 3}\) | \(0\) | \(\frac{ 1}{ 3}\) | \(\frac{ 1}{ 3}\) | \(\frac{ 5}{ 3}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 5}{ 3}\) |
| \(\frac{ 4}{ 3}\) | \(\frac{ 4}{ 3}\) | \(0\) | \(\frac{ 4}{ 3}\) | \(\frac{ 4}{ 3}\) | \(\frac{ 8}{ 3}\) |
3
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:...
\((4z-1)(4z+1)(16z^2+4z+1)(640z^3+96z^2+48z-1)(1+6z-48z^2+320z^3)^2\)
| \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 8}-\frac{ 1}{ 8}\sqrt{ 3}I\) | \(-\frac{ 1}{ 8}+\frac{ 1}{ 8}\sqrt{ 3}I\) | ≈\(-0.084967-0.266773I\) | ≈\(-0.084967+0.266773I\) | ≈\(-0.082432\) | \(0\) | ≈\(0.019933\) | ≈\(0.116216-0.156217I\) | ≈\(0.116216+0.156217I\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) | \(3\) | \(1\) | \(2\) |
| \(2\) | \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) | \(4\) | \(2\) | \(3\) |
4
New Number: 8.4 | AESZ: 160 | Superseeker: 6 -325 | Hash: 8ce8667fe6e49ce6625fafe044b1641b
Degree: 8
\(\theta^4-3 x(3\theta^2+3\theta+1)(7\theta^2+7\theta+2)+3^{2} x^{2}\left(171\theta^4+396\theta^3+555\theta^2+318\theta+64\right)-2^{3} 3^{4} x^{3}\left(21\theta^4-126\theta^3-386\theta^2-291\theta-76\right)+2^{4} 3^{5} x^{4}\left(147\theta^4+294\theta^3+102\theta^2-45\theta-14\right)+2^{6} 3^{7} x^{5}\left(21\theta^4+210\theta^3+118\theta^2-19\theta-24\right)+2^{6} 3^{8} x^{6}\left(171\theta^4+288\theta^3+393\theta^2+288\theta+76\right)+2^{9} 3^{10} x^{7}(3\theta^2+3\theta+1)(7\theta^2+7\theta+2)+2^{12} 3^{12} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, 90, 1176, 3114, ... --> OEIS Normalized instanton numbers (n0=1): 6, 6, -325, -1977/2, -5421, ... ; Common denominator:...
\((27z^2+9z+1)(1728z^2-72z+1)(1+216z^2)^2\)
| \(-\frac{ 1}{ 6}-\frac{ 1}{ 18}\sqrt{ 3}I\) | \(-\frac{ 1}{ 6}+\frac{ 1}{ 18}\sqrt{ 3}I\) | \(0-\frac{ 1}{ 36}\sqrt{ 6}I\) | \(0\) | \(0+\frac{ 1}{ 36}\sqrt{ 6}I\) | \(\frac{ 1}{ 48}-\frac{ 1}{ 144}\sqrt{ 3}I\) | \(\frac{ 1}{ 48}+\frac{ 1}{ 144}\sqrt{ 3}I\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(2\) | \(1\) |
5
New Number: 24.4 | AESZ: | Superseeker: 6 -32282291/54 | Hash: b98c7f29efec34446d8add48441fa228
Degree: 24
\(\theta^4-3 x\left(11\theta^4+34\theta^3+32\theta^2+15\theta+3\right)+3^{2} x^{2}\left(27\theta^4+733966\theta^3+171\right)+3^{3} x^{3}\left(2926\theta^4-5560\theta^3-16480\theta^2-11928\theta-3735\right)-3^{4} x^{4}\left(30606\theta^4+32760\theta^3-132070\theta^2-121130\theta-44307\right)+3^{6} x^{5}\left(15750\theta^4+248992\theta^3-218660\theta^2-267352\theta-113937\right)+3^{7} x^{6}\left(447390\theta^4-1611064\theta^3+997138\theta^2+1525654\theta+737721\right)-3^{8} x^{7}\left(4210518\theta^4-4046728\theta^3+6791528\theta^2+9988640\theta+5160861\right)+3^{9} x^{8}\left(16918876\theta^4+1291896\theta^3+31887842\theta^2+47907054\theta+27066537\right)-3^{11} x^{9}\left(5747912\theta^4-10506476\theta^3-26158764\theta^2-16601042\theta-464415\right)-3^{12} x^{10}\left(52637104\theta^4+232675688\theta^3+616661120\theta^2+721851010\theta+337522383\right)+3^{13} x^{11}\left(277041602\theta^4+1204855368\theta^3+2973647056\theta^2+35822628224\theta+1740716235\right)-3^{15} x^{12}\left(156460502\theta^4+624228888\theta^3+1065193690\theta^2+810960198\theta+193208541\right)-3^{16} x^{13}\left(238576054\theta^4+2173084944\theta^3+8426851964\theta^2+14067417072\theta+8577791883\right)+3^{17} x^{14}\left(1561753522\theta^4+11510031576\theta^3+37524000206\theta^2+58271908434\theta+34413775443\right)-3^{19} x^{15}\left(675921878\theta^4+4776222328\theta^3+14788847224\theta^2+23325064352\theta+14445727221\right)-3^{21} x^{16}\left(332578151\theta^4+2930405144\theta^3+10261391450\theta^2+15302524086\theta+8113699269\right)+3^{24} x^{17}\left(135646615\theta^4+1173472306\theta^3+4199227068\theta^2+6859331311\theta+4126872408\right)-3^{25} x^{18}\left(52966465\theta^4+612076328\theta^3+3045213907\theta^2+6814044204\theta+5181429744\right)-2^{3} 3^{27} x^{19}\left(9827313\theta^4+76454094\theta^3+203071208\theta^2+155130637\theta-15471658\right)+2^{4} 3^{29} x^{20}\left(1601399\theta^4+15660570\theta^3+55267842\theta^2+71870481\theta+28392908\right)+2^{6} 3^{31} x^{21}\left(101735\theta^4+542938\theta^3+535032\theta^2-332573\theta-382670\right)-2^{6} 3^{33} x^{22}\left(45889\theta^4+396580\theta^3+1148993\theta^2+1448570\theta+695584\right)-2^{9} 3^{35} 5 x^{23}\left(87\theta^4+138\theta^3-716\theta^2-2001\theta-1376\right)+2^{12} 3^{37} 5^{2} x^{24}\left((\theta+2)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 9, 513/8, -5851781/8, -32364933705/1024, ... --> OEIS Normalized instanton numbers (n0=1): 6, -1965/16, -32282291/54, 234744298799/32768, 976987022211008331/8000000, ... ; Common denominator:...
\(1-33z-16326382741674649276608z^22-11143025724449214743040z^23+46109071963238129971200z^24+978441930z^6-27625208598z^7+333014236308z^8-1018225367064z^9-27973515186864z^10-3478884927060667653z^16+38310610599666661815z^17+243z^2+79002z^3-2479086z^4+11481750z^5-44877882476961328995z^18+441693798025446z^11-2245037192371314z^12-10269916833818934z^13+201685104396904086z^14-785597953501675026z^15-599513066375840399448z^19+1758473882907940341072z^20+4021696190140630274880z^21\)
No data for singularities
6
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