1
New Number: 10.10 | AESZ: | Superseeker: 28/3 83612/81 | Hash: 8270c1ecc701d7cbd422a656c6118587
Degree: 10
\(3^{2} \theta^4+2^{2} 3 x\left(220\theta^4+152\theta^3+207\theta^2+131\theta+31\right)+2^{4} x^{2}\left(20608\theta^4+32896\theta^3+50132\theta^2+37496\theta+11991\right)+2^{8} x^{3}\left(89936\theta^4+243168\theta^3+429080\theta^2+391080\theta+152645\right)+2^{12} x^{4}\left(242448\theta^4+966912\theta^3+2030168\theta^2+2199488\theta+1002377\right)+2^{20} x^{5}\left(26320\theta^4+142696\theta^3+359216\theta^2+454946\theta+237357\right)+2^{23} x^{6}\left(59600\theta^4+415872\theta^3+1247376\theta^2+1826640\theta+1079063\right)+2^{28} x^{7}\left(21712\theta^4+187424\theta^3+661000\theta^2+1107048\theta+733353\right)+2^{32} x^{8}\left(9744\theta^4+100992\theta^3+412312\theta^2+779936\theta+572857\right)+2^{39} x^{9}\left(304\theta^4+3696\theta^3+17208\theta^2+36300\theta+29211\right)+2^{44} x^{10}\left((2\theta+7)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -124/3, 1220, -872528/27, 67351172/81, ... --> OEIS Normalized instanton numbers (n0=1): 28/3, -695/9, 83612/81, -4447894/243, 274874464/729, ... ; Common denominator:...
\((1+48z+256z^2)(32z+1)^2(16z+1)^2(32z+3)^2(64z+1)^2\)
| \(-\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(-\frac{ 3}{ 32}\) | \(-\frac{ 1}{ 16}\) | \(-\frac{ 1}{ 32}\) | \(-\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(-\frac{ 1}{ 64}\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 7}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(0\) | \(1\) | \(1\) | \(0\) | \(\frac{ 7}{ 2}\) |
| \(1\) | \(-2\) | \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(\frac{ 7}{ 2}\) |
| \(2\) | \(3\) | \(1\) | \(1\) | \(2\) | \(4\) | \(0\) | \(\frac{ 7}{ 2}\) |
2
New Number: 10.9 | AESZ: | Superseeker: 4 116 | Hash: dbcf215f85612454543d472ffd3bffa9
Degree: 10
\(\theta^4-2^{2} x\left(38\theta^4+70\theta^3+93\theta^2+58\theta+14\right)+2^{4} x^{2}\left(609\theta^4+2214\theta^3+4255\theta^2+4118\theta+1630\right)-2^{8} x^{3}\left(1357\theta^4+7284\theta^3+18055\theta^2+22233\theta+11143\right)+2^{10} x^{4}\left(7450\theta^4+52316\theta^3+157665\theta^2+230387\theta+134924\right)-2^{14} x^{5}\left(6580\theta^4+56446\theta^3+198857\theta^2+332342\theta+219249\right)+2^{16} x^{6}\left(15153\theta^4+151710\theta^3+606095\theta^2+1128594\theta+818733\right)-2^{20} x^{7}\left(5621\theta^4+63496\theta^3+280382\theta^2+568755\theta+444393\right)+2^{22} x^{8}\left(5152\theta^4+63904\theta^3+304853\theta^2+659693\theta+544236\right)-2^{26} 3 x^{9}\left(220\theta^4+2928\theta^3+14781\theta^2+33462\theta+28605\right)+2^{28} 3^{2} x^{10}\left((2\theta+7)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 56, 2192, 74112, 2319376, ... --> OEIS Normalized instanton numbers (n0=1): 4, 31/2, 116, 2477/2, 16876, ... ; Common denominator:...
\((1-48z+256z^2)(4z-1)^2(24z-1)^2(8z-1)^2(16z-1)^2\)
| \(0\) | \(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 24}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 8}\) | \(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 7}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(0\) | \(0\) | \(1\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(0\) | \(1\) | \(-2\) | \(1\) | \(1\) | \(1\) | \(3\) | \(\frac{ 7}{ 2}\) |
| \(0\) | \(2\) | \(3\) | \(1\) | \(1\) | \(2\) | \(4\) | \(\frac{ 7}{ 2}\) |
3
New Number: 13.13 | AESZ: | Superseeker: 32 74144 | Hash: e20067c633b6371dc19f760a1140f0e4
Degree: 13
\(\theta^4-2^{3} x\left(74\theta^4+52\theta^3+70\theta^2+44\theta+11\right)+2^{6} x^{2}\left(1948\theta^4+2320\theta^3+3750\theta^2+3244\theta+1117\right)-2^{11} x^{3}\left(5498\theta^4+9708\theta^3+17699\theta^2+12099\theta+2024\right)+2^{12} x^{4}\left(90192\theta^4+243456\theta^3+317216\theta^2-2080\theta-132883\right)+2^{16} x^{5}\left(35024\theta^4+171680\theta^3+1168736\theta^2+2029296\theta+1162051\right)-2^{20} x^{6}\left(249200\theta^4+1529280\theta^3+3887240\theta^2+5111280\theta+2830091\right)+2^{24} x^{7}\left(6224\theta^4+297952\theta^3+1078344\theta^2+1331848\theta+442349\right)+2^{29} x^{8}\left(78896\theta^4+725696\theta^3+2501496\theta^2+3908720\theta+2314163\right)+2^{34} x^{9}\left(9584\theta^4+62208\theta^3+120960\theta^2+36216\theta-71103\right)+2^{38} x^{10}\left(2864\theta^4+44992\theta^3+291624\theta^2+843472\theta+893907\right)-2^{42} x^{11}\left(8176\theta^4+131296\theta^3+780536\theta^2+2035976\theta+1968867\right)-2^{47} 3 x^{12}\left(752\theta^4+11328\theta^3+62952\theta^2+153648\theta+139383\right)-2^{52} 3^{2} x^{13}\left((2\theta+7)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 88, 6576, 475776, 37804816, ... --> OEIS Normalized instanton numbers (n0=1): 32, 1048, 74144, 7046865, 788076384, ... ; Common denominator:...
\(-(16z-1)(262144z^4-8192z^3+2304z^2-256z+1)(48z-1)^2(16z+1)^2(512z^2+128z-1)^2\)
| \(-\frac{ 1}{ 8}-\frac{ 3}{ 32}\sqrt{ 2}\) | \(-\frac{ 1}{ 16}\) | ≈\(-0.024399\) | ≈\(-0.024399\) | \(0\) | ≈\(0.004052\) | \(-\frac{ 1}{ 8}+\frac{ 3}{ 32}\sqrt{ 2}\) | \(\frac{ 1}{ 48}\) | \(\frac{ 1}{ 16}\) | ≈\(0.075996\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 7}{ 2}\) |
| \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(-2\) | \(1\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(4\) | \(1\) | \(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(3\) | \(2\) | \(2\) | \(\frac{ 7}{ 2}\) |
4
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:...
\(-(8z-1)(1024z^4-2048z^3+144z^2-4z+1)(8z-3)^2(8z+1)^2(32z^2-32z-1)^2\)
| \(-\frac{ 1}{ 8}\) | \(\frac{ 1}{ 2}-\frac{ 3}{ 8}\sqrt{ 2}\) | ≈\(-0.015388\) | ≈\(-0.015388\) | \(0\) | ≈\(0.102801\) | \(\frac{ 1}{ 8}\) | \(\frac{ 3}{ 8}\) | \(\frac{ 1}{ 2}+\frac{ 3}{ 8}\sqrt{ 2}\) | ≈\(1.927975\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 7}{ 2}\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(-2\) | \(3\) | \(1\) | \(\frac{ 7}{ 2}\) |
| \(1\) | \(4\) | \(2\) | \(2\) | \(0\) | \(2\) | \(2\) | \(3\) | \(4\) | \(2\) | \(\frac{ 7}{ 2}\) |