1
New Number: 3.1 | AESZ: 34 | Superseeker: 1 28/3 | Hash: e5461c5f5ae4d929328f66b8955a31f5
Degree: 3
\(\theta^4-x\left(35\theta^4+70\theta^3+63\theta^2+28\theta+5\right)+x^{2}(\theta+1)^2(259\theta^2+518\theta+285)-3^{2} 5^{2} x^{3}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 5, 45, 545, 7885, ... --> OEIS Normalized instanton numbers (n0=1): 1, 2, 28/3, 52, 350, ... ; Common denominator:...
\(-(z-1)(25z-1)(9z-1)\)
| \(0\) | \(\frac{ 1}{ 25}\) | \(\frac{ 1}{ 9}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(2\) |
| \(0\) | \(2\) | \(2\) | \(2\) | \(2\) |
2
New Number: 5.17 | AESZ: 119 | Superseeker: 28/3 3892/3 | Hash: dc8ec37012f2c92c83e6519935956eeb
Degree: 5
\(3^{2} \theta^4-2^{2} 3 x\left(256\theta^4+320\theta^3+271\theta^2+111\theta+18\right)+2^{7} x^{2}\left(3104\theta^4+7040\theta^3+8012\theta^2+4452\theta+927\right)-2^{15} x^{3}\left(752\theta^4+2304\theta^3+3042\theta^2+1854\theta+405\right)+2^{21} x^{4}(2\theta+1)(176\theta^3+552\theta^2+622\theta+231)-2^{31} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 24, 1128, 67200, 4634280, ... --> OEIS Normalized instanton numbers (n0=1): 28/3, 394/3, 3892/3, 108262/3, 1044128, ... ; Common denominator:...
\(-(-1+128z)(64z-1)^2(128z-3)^2\)
| \(0\) | \(\frac{ 1}{ 128}\) | \(\frac{ 1}{ 64}\) | \(\frac{ 3}{ 128}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(\frac{ 1}{ 4}\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(\frac{ 3}{ 4}\) | \(3\) | \(1\) |
| \(0\) | \(2\) | \(1\) | \(4\) | \(\frac{ 3}{ 2}\) |
3
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:...
\((1+48z+256z^2)(32z+1)^2(16z+1)^2(32z+3)^2(64z+1)^2\)
| \(-\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(-\frac{ 3}{ 32}\) | \(-\frac{ 1}{ 16}\) | \(-\frac{ 1}{ 32}\) | \(-\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(-\frac{ 1}{ 64}\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 7}{ 2}\) |
| \(1\) | \(1\) | \(0\) | \(0\) | \(1\) | \(1\) | \(0\) | \(\frac{ 7}{ 2}\) |
| \(1\) | \(-2\) | \(1\) | \(1\) | \(1\) | \(3\) | \(0\) | \(\frac{ 7}{ 2}\) |
| \(2\) | \(3\) | \(1\) | \(1\) | \(2\) | \(4\) | \(0\) | \(\frac{ 7}{ 2}\) |
4
New Number: 16.17 | AESZ: | Superseeker: 28/3 36092/81 | Hash: 5149f445650e5115373b6acb592ca441
Degree: 16
\(3^{2} \theta^4-2 3 x\left(52\theta^4+212\theta^3+180\theta^2+74\theta+13\right)-2^{2} x^{2}\left(1928\theta^4-11512\theta^3-22670\theta^2-14864\theta-4047\right)+2^{5} x^{3}\left(16640\theta^4+29388\theta^3-33444\theta^2-40977\theta-16934\right)-2^{4} x^{4}\left(121856\theta^4+2127712\theta^3-49464\theta^2-814568\theta-411697\right)-2^{7} x^{5}\left(1578640\theta^4-965264\theta^3-363000\theta^2+278728\theta+480205\right)+2^{10} x^{6}\left(2533416\theta^4+2287224\theta^3+3521090\theta^2+3792864\theta+1769631\right)-2^{13} x^{7}\left(344968\theta^4+674036\theta^3+1363902\theta^2+1918853\theta+1331406\right)-2^{12} x^{8}\left(15242656\theta^4+70247008\theta^3+154128344\theta^2+170540504\theta+76073233\right)+2^{16} x^{9}\left(3745592\theta^4+24132312\theta^3+70149744\theta^2+101813004\theta+60063611\right)+2^{18} x^{10}\left(365384\theta^4+3028648\theta^3+5006034\theta^2-6421376\theta-15599999\right)-2^{21} x^{11}\left(1103728\theta^4+11350204\theta^3+44360888\theta^2+78097451\theta+52598648\right)+2^{20} x^{12}\left(3809536\theta^4+47933664\theta^3+233170440\theta^2+516785976\theta+438059199\right)-2^{23} x^{13}\left(183664\theta^4+3018320\theta^3+17505384\theta^2+43640024\theta+40050861\right)-2^{26} x^{14}\left(8168\theta^4+101912\theta^3+453794\theta^2+849648\theta+551615\right)-2^{29} x^{15}\left(8\theta^4-228\theta^3-2714\theta^2-9345\theta-10420\right)+2^{28} x^{16}\left((2\theta+7)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 26/3, 238/3, 14476/27, -527902/81, ... --> OEIS Normalized instanton numbers (n0=1): 28/3, -497/9, 36092/81, -6997057/972, 74043424/729, ... ; Common denominator:...
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No data for singularities