1
New Number: 14.11 | AESZ: | Superseeker: 52/5 13436/5 | Hash: c3784675984d5e6eac952e2484ce5404
Degree: 14
\(5^{2} \theta^4-2^{2} 5 x\left(104\theta^4+256\theta^3+483\theta^2+355\theta+95\right)-2^{4} x^{2}\left(416\theta^4-4672\theta^3+2816\theta^2+12600\theta+7865\right)+2^{10} x^{3}\left(3248\theta^4+17808\theta^3+48534\theta^2+70980\theta+43885\right)-2^{12} x^{4}\left(1024\theta^4+36416\theta^3+105744\theta^2+110264\theta+16363\right)-2^{18} x^{5}\left(8760\theta^4+76704\theta^3+282893\theta^2+513127\theta+376109\right)-2^{21} 3 x^{6}\left(888\theta^4+896\theta^3-8544\theta^2-17976\theta-2111\right)+2^{28} x^{7}\left(2848\theta^4+34496\theta^3+165049\theta^2+366072\theta+314912\right)+2^{29} x^{8}\left(10216\theta^4+125440\theta^3+627568\theta^2+1479624\theta+1370831\right)-2^{34} x^{9}\left(5720\theta^4+84576\theta^3+485065\theta^2+1262925\theta+1248247\right)-2^{36} x^{10}\left(16640\theta^4+273472\theta^3+1728064\theta^2+4911896\theta+5256897\right)+2^{42} x^{11}\left(336\theta^4+1392\theta^3-16378\theta^2-112292\theta-182997\right)+2^{44} x^{12}\left(2720\theta^4+43584\theta^3+258352\theta^2+671784\theta+646989\right)+2^{50} 3 x^{13}\left(8\theta^4+256\theta^3+2199\theta^2+7393\theta+8717\right)-2^{56} 3^{2} x^{14}\left((\theta+4)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 76, 5228, 322224, 18933228, ... --> OEIS Normalized instanton numbers (n0=1): 52/5, 115, 13436/5, 89632, 18465296/5, ... ; Common denominator:...
\(-(-1+16z)(48z-1)^2(256z^2-32z-5)^2(256z^2+16z-1)^2(16z+1)^3\)
| \(-\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 16}-\frac{ 1}{ 16}\sqrt{ 6}\) | \(-\frac{ 1}{ 16}\) | \(0\) | \(\frac{ 1}{ 48}\) | \(-\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 16}+\frac{ 1}{ 16}\sqrt{ 6}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(4\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(0\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(4\) |
| \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(0\) | \(-2\) | \(\frac{ 1}{ 2}\) | \(1\) | \(3\) | \(4\) |
| \(1\) | \(4\) | \(0\) | \(0\) | \(3\) | \(1\) | \(2\) | \(4\) | \(4\) |
2
New Number: 15.4 | AESZ: | Superseeker: 52/5 13436/5 | Hash: 2306e85a3af0a97d616dedf03cc93f69
Degree: 15
\(5^{2} \theta^4-2^{2} 5 x\left(524\theta^4+56\theta^3+83\theta^2+55\theta+15\right)+2^{4} x^{2}\left(122784\theta^4+39552\theta^3+60584\theta^2+42560\theta+9895\right)-2^{8} x^{3}\left(851424\theta^4+544704\theta^3+819724\theta^2+563860\theta+144605\right)+2^{13} x^{4}\left(1949840\theta^4+2047744\theta^3+3062224\theta^2+2155304\theta+617905\right)-2^{18} x^{5}\left(3117952\theta^4+4806720\theta^3+7335648\theta^2+5468420\theta+1717063\right)+2^{22} x^{6}\left(7179524\theta^4+15086448\theta^3+24112808\theta^2+19319920\theta+6533401\right)-2^{26} x^{7}\left(12098492\theta^4+32868584\theta^3+56087648\theta^2+48438116\theta+17467537\right)+2^{31} x^{8}\left(7508036\theta^4+25345280\theta^3+46719420\theta^2+43397656\theta+16591239\right)-2^{38} x^{9}\left(856369\theta^4+3481940\theta^3+6970670\theta^2+6938899\theta+2800514\right)+2^{42} x^{10}\left(568775\theta^4+2715196\theta^3+5906890\theta^2+6274274\theta+2662654\right)-2^{46} x^{11}\left(269591\theta^4+1478382\theta^3+3484287\theta^2+3929620\theta+1745534\right)+2^{51} x^{12}\left(44091\theta^4+272424\theta^3+691403\theta^2+822862\theta+380404\right)-2^{57} x^{13}\left(2349\theta^4+16068\theta^3+43548\theta^2+54271\theta+25924\right)+2^{63} x^{14}\left(73\theta^4+544\theta^3+1559\theta^2+2017\theta+988\right)-2^{69} x^{15}\left((\theta+2)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 44, -3792, -207124, ... --> OEIS Normalized instanton numbers (n0=1): 52/5, 115, 13436/5, 89632, 18465296/5, ... ; Common denominator:...
\(-(-1+32z)(256z^2-48z+1)^2(512z^2-128z+5)^2(64z-1)^3(16z-1)^3\)
| \(0\) | \(\frac{ 1}{ 64}\) | \(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 32}\) | \(\frac{ 1}{ 8}-\frac{ 1}{ 32}\sqrt{ 6}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 8}+\frac{ 1}{ 32}\sqrt{ 6}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(2\) |
| \(0\) | \(2\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(1\) | \(2\) |
| \(0\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(3\) | \(0\) | \(\frac{ 1}{ 2}\) | \(3\) | \(2\) |
| \(0\) | \(5\) | \(1\) | \(2\) | \(4\) | \(0\) | \(1\) | \(4\) | \(2\) |
3
New Number: 24.3 | AESZ: | Superseeker: 52/5 5899/5 | Hash: d0e287eaa4fef980c189e2ff531cfe15
Degree: 24
\(5^{2} \theta^4-5 x\left(491\theta^4+934\theta^3+722\theta^2+255\theta+35\right)+x^{2}\left(7159\theta^4+6232\theta^3-12151\theta^2-20470\theta-7105\right)+x^{3}\left(18758\theta^4+85536\theta^3+125256\theta^2+44940\theta+9625\right)+x^{4}\left(107306\theta^4-465824\theta^3-1781630\theta^2-1509010\theta-420741\right)-x^{5}\left(740094\theta^4-1297608\theta^3-5441440\theta^2+261976\theta+1419015\right)-x^{6}\left(425070\theta^4+2630928\theta^3-1828778\theta^2-9227454\theta-5729271\right)+x^{7}\left(2418550\theta^4+20716304\theta^3-31322144\theta^2-45688692\theta-18761303\right)+x^{8}\left(12130172\theta^4-80918752\theta^3+123192250\theta^2+111390334\theta+20525227\right)-x^{9}\left(17292844\theta^4-87187836\theta^3+258415980\theta^2+122394558\theta-28117691\right)-x^{10}\left(77350272\theta^4-52258560\theta^3-209801740\theta^2+35556398\theta+112842235\right)+x^{11}\left(169708186\theta^4-275075696\theta^3-61487240\theta^2+173105868\theta+132064403\right)+x^{12}\left(10381942\theta^4+721961664\theta^3+662207782\theta^2+449099274\theta+145105369\right)-x^{13}\left(297104050\theta^4+976538840\theta^3+1274259392\theta^2+987704752\theta+327432741\right)+x^{14}\left(221581518\theta^4+18861264\theta^3-741766394\theta^2-1393177990\theta-797694603\right)+x^{15}\left(114705522\theta^4+1320217008\theta^3+3568249520\theta^2+4492131828\theta+2173936059\right)-x^{16}\left(224356709\theta^4+1230081376\theta^3+2802678530\theta^2+3051898566\theta+1307246399\right)+x^{17}\left(65530931\theta^4+95408210\theta^3-252661082\theta^2-914043647\theta-686884832\right)+x^{18}\left(56745577\theta^4+512911848\theta^3+1706476923\theta^2+2593842540\theta+1461946064\right)-2^{3} x^{19}\left(5403673\theta^4+39411950\theta^3+129809978\theta^2+200689723\theta+116245602\right)+2^{4} x^{20}\left(169515\theta^4+1407570\theta^3+7987370\theta^2+18253981\theta+13483356\right)+2^{6} x^{21}\left(97217\theta^4+692142\theta^3+1820686\theta^2+1961919\theta+708018\right)-2^{6} 3 x^{22}\left(8565\theta^4+73588\theta^3+231589\theta^2+312066\theta+153136\right)-2^{9} 3^{2} x^{23}\left(51\theta^4+242\theta^3+354\theta^2+101\theta-88\right)+2^{12} 3^{3} x^{24}\left((\theta+2)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 7, 231, 10787, 606497, ... --> OEIS Normalized instanton numbers (n0=1): 52/5, 677/10, 5899/5, 273031/10, 3873518/5, ... ; Common denominator:...
\((z-1)(z^2+z-1)(64z^6-328z^5+603z^4-336z^3-82z^2+96z-1)(z+1)^2(8z^5+8z^4-37z^3+47z^2+17z+5)^2(3z-1)^3\)
No data for singularities