1
New Number: 13.14 | AESZ: | Superseeker: 20/3 36340/81 | Hash: 4b391bfc7d7d7a60edd430907aff9fae
Degree: 13
\(3^{2} \theta^4+2^{2} 3 x\left(47\theta^4-50\theta^3-45\theta^2-20\theta-4\right)+2^{4} x^{2}\left(511\theta^4-1052\theta^3+179\theta^2+302\theta+132\right)-2^{7} x^{3}\left(179\theta^4-306\theta^3+1857\theta^2+2226\theta+931\right)-2^{8} x^{4}\left(2396\theta^4+17992\theta^3+43050\theta^2+42004\theta+13733\right)-2^{10} x^{5}\left(19724\theta^4+94712\theta^3+170136\theta^2+115772\theta+521\right)-2^{12} x^{6}\left(1556\theta^4-52704\theta^3-398172\theta^2-916440\theta-712527\right)+2^{15} x^{7}\left(62300\theta^4+489880\theta^3+1536500\theta^2+2159040\theta+1096749\right)-2^{18} x^{8}\left(8756\theta^4+79664\theta^3+485090\theta^2+1462308\theta+1567885\right)-2^{20} x^{9}\left(45096\theta^4+509616\theta^3+2195020\theta^2+4371756\theta+3428277\right)+2^{22} x^{10}\left(43984\theta^4+538112\theta^3+2558944\theta^2+5583456\theta+4682427\right)-2^{25} x^{11}\left(7792\theta^4+99808\theta^3+490272\theta^2+1087312\theta+914209\right)+2^{28} x^{12}\left(592\theta^4+7872\theta^3+39704\theta^2+89808\theta+76717\right)-2^{31} x^{13}\left((2\theta+7)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16/3, 52/3, 3200/27, 129668/81, ... --> OEIS Normalized instanton numbers (n0=1): 20/3, -410/9, 36340/81, -5386783/972, 57719264/729, ... ; Common denominator:...
\(-(8z-1)(1024z^4-2048z^3+144z^2-4z+1)(8z-3)^2(8z+1)^2(32z^2-32z-1)^2\)
| \(-\frac{ 1}{ 8}\) | \(\frac{ 1}{ 2}-\frac{ 3}{ 8}\sqrt{ 2}\) | ≈\(-0.015388\) | ≈\(-0.015388\) | \(0\) | ≈\(0.102801\) | \(\frac{ 1}{ 8}\) | \(\frac{ 3}{ 8}\) | \(\frac{ 1}{ 2}+\frac{ 3}{ 8}\sqrt{ 2}\) | ≈\(1.927975\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 7}{ 2}\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(-2\) | \(3\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(1\) | \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(3\) | \(4\) | \(2\) | \(\frac{ 7}{ 2}\) |
2
New Number: 16.7 | AESZ: | Superseeker: 20/3 -21368/81 | Hash: ed36d7830ecca61b6e5c113a96a492a0
Degree: 16
\(2^{4} 3^{2} \theta^4-2^{3} 3 x\left(488\theta^4+868\theta^3+702\theta^2+268\theta+41\right)+2^{2} x^{2}\left(92032\theta^4+264232\theta^3+340334\theta^2+184604\theta+35871\right)-2^{2} x^{3}\left(1072240\theta^4+840696\theta^3-1802904\theta^2-2109510\theta-795037\right)-x^{4}\left(117110904\theta^2+178119592\theta-76769344\theta^4-109952288\theta^3+56644559\right)-2^{3} x^{5}\left(39653720\theta^4-41464324\theta^3-49511586\theta^2-19633210\theta+8561249\right)+2 x^{6}\left(1911091072\theta^4-560017392\theta^3-1782035460\theta^2-675901440\theta-3110721\right)+2^{2} x^{7}\left(608631376\theta^4+1765102952\theta^3+2652375136\theta^2+1439834874\theta+142764075\right)-x^{8}\left(24186241888\theta^3+31220323448\theta+40121480696\theta^2+8617369041+6553002016\theta^4\right)-2^{3} x^{9}\left(559057576\theta^4+3711601476\theta^3+11096418710\theta^2+16005760200\theta+9042841485\right)+2^{3} 3^{2} x^{10}\left(27337088\theta^4+184901916\theta^3+441638533\theta^2+358787334\theta-3513990\right)+2^{2} 3 x^{11}\left(190509712\theta^4+1956311176\theta^3+7797884008\theta^2+14187472734\theta+9913342473\right)+3^{2} x^{12}\left(76860224\theta^4+1038528096\theta^3+5131794968\theta^2+11168867880\theta+9129957831\right)+2^{3} 3^{2} x^{13}\left(1042424\theta^4+19906060\theta^3+129088894\theta^2+352019522\theta+349060761\right)-2 3^{3} x^{14}\left(119168\theta^4+772592\theta^3-1179292\theta^2-15270480\theta-24272433\right)-2^{2} 3^{4} x^{15}\left(5264\theta^4+89736\theta^3+539056\theta^2+1386618\theta+1305315\right)+3^{8} x^{16}\left((2\theta+7)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 41/6, 2549/24, 666089/432, 84731131/10368, ... --> OEIS Normalized instanton numbers (n0=1): 20/3, -55/18, -21368/81, -562673/486, -6431620/729, ... ; Common denominator:...
\(\)
No data for singularities
3
New Number: 24.16 | AESZ: | Superseeker: 20/3 7540/81 | Hash: 9b288a17ff21e31512fe3730227152b2
Degree: 24
\(3^{3} \theta^4-2^{2} 3^{2} x\left(51\theta^4+94\theta^3+81\theta^2+34\theta+6\right)+2^{4} 3 x^{2}\left(777\theta^4+3952\theta^3+5495\theta^2+3326\theta+840\right)+2^{6} x^{3}\left(6076\theta^4-36580\theta^3-96208\theta^2-73820\theta-22971\right)-2^{8} x^{4}\left(91962\theta^4+92760\theta^3-287340\theta^2-275194\theta-88617\right)+2^{10} x^{5}\left(255290\theta^4+840624\theta^3-841718\theta^2-1139664\theta-435957\right)+2^{12} x^{6}\left(344350\theta^4-2037616\theta^3+2302248\theta^2+3899366\theta+1855473\right)-2^{14} x^{7}\left(3596934\theta^4-1919904\theta^3+4846554\theta^2+7817604\theta+3815689\right)+2^{16} x^{8}\left(8122336\theta^4-2455824\theta^3+1743468\theta^2+4576350\theta+2211269\right)-2^{18} x^{9}\left(4736512\theta^4-15179116\theta^3-30014900\theta^2-27517140\theta-10151379\right)-2^{20} x^{10}\left(10049328\theta^4+43157856\theta^3+84407914\theta^2+77408798\theta+27100963\right)+2^{22} x^{11}\left(16849298\theta^4+43081512\theta^3+66129374\theta^2+42478644\theta+5863649\right)-2^{24} x^{12}\left(2120418\theta^4-19095648\theta^3-77625292\theta^2-120132994\theta-66210663\right)-2^{26} x^{13}\left(11329982\theta^4+59772152\theta^3+148599750\theta^2+178534328\theta+82729387\right)+2^{28} x^{14}\left(5764462\theta^4+18211776\theta^3+27275956\theta^2+15555738\theta+1058615\right)+2^{30} x^{15}\left(2768822\theta^4+19152112\theta^3+48724938\theta^2+52160308\theta+17451325\right)-2^{32} x^{16}\left(2326731\theta^4+9250224\theta^3+12025644\theta^2-5312634\theta-13944959\right)-2^{34} x^{17}\left(238805\theta^4+1852302\theta^3+1102491\theta^2-7080654\theta-8783903\right)+2^{36} x^{18}\left(377045\theta^4+632272\theta^3-4486531\theta^2-16948308\theta-14739201\right)+2^{39} x^{19}\left(16533\theta^4+234894\theta^3+875221\theta^2+1653596\theta+1206823\right)-2^{42} x^{20}\left(5449\theta^4-48270\theta^3-337532\theta^2-586347\theta-302891\right)-2^{44} x^{21}\left(2935\theta^4+30482\theta^3+120769\theta^2+177402\theta+84039\right)-2^{46} x^{22}\left(179\theta^4+6980\theta^3+3029\theta^2+47490\theta+25879\right)+2^{49} 5 x^{23}\left(47\theta^4+378\theta^3+1119\theta^2+1464\theta+719\right)+2^{52} 5^{2} x^{24}\left((\theta+2)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 84, 864, 4164, ... --> OEIS Normalized instanton numbers (n0=1): 20/3, -194/9, 7540/81, -2021323/972, 1669749088/91125, ... ; Common denominator:...
\((4z+1)(16z^2+4z-1)(16384z^6+10240z^5+9984z^4+1024z^3-1056z^2+56z-1)(4z-1)^2(10240z^5-8704z^4+2752z^3-176z^2-4z+1)^2(4z+3)^3\)
No data for singularities