1
New Number: 4.33 | AESZ: 55 | Superseeker: 76/3 144196/3 | Hash: 7e88cd5b7dc1c51022b66ac6f009218f
Degree: 4
\(3^{2} \theta^4-2^{2} 3 x\left(208\theta^4+224\theta^3+163\theta^2+51\theta+6\right)+2^{9} x^{2}\left(32\theta^4-928\theta^3-1606\theta^2-837\theta-141\right)+2^{16} x^{3}\left(144\theta^4+576\theta^3+467\theta^2+144\theta+15\right)-2^{24} x^{4}\left((2\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 936, 108800, 16748200, ... --> OEIS Normalized instanton numbers (n0=1): 76/3, 3476/3, 144196/3, 3563196, 309069600, ... ; Common denominator:...
\(-(64z+1)(256z-1)(-3+128z)^2\)
| \(-\frac{ 1}{ 64}\) | \(0\) | \(\frac{ 1}{ 256}\) | \(\frac{ 3}{ 128}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) |
| \(2\) | \(0\) | \(2\) | \(4\) | \(\frac{ 1}{ 2}\) |
2
New Number: 13.12 | AESZ: | Superseeker: 76/3 746444/81 | Hash: fec1670f7378fb309308803574ce2a00
Degree: 13
\(3^{2} \theta^4+2^{2} 3 x\left(4\theta^4-208\theta^3-189\theta^2-85\theta-17\right)-2^{4} x^{2}\left(5120\theta^4-7168\theta^3-21704\theta^2-15788\theta-5307\right)+2^{9} x^{3}\left(6080\theta^4+28992\theta^3-21720\theta^2-27270\theta-13529\right)+2^{12} x^{4}\left(40096\theta^4-258688\theta^3-41760\theta^2+16820\theta+38071\right)-2^{17} x^{5}\left(123088\theta^4-63104\theta^3+45236\theta^2+55562\theta+46257\right)+2^{21} x^{6}\left(219712\theta^4+380352\theta^3+753688\theta^2+810222\theta+409897\right)-2^{24} x^{7}\left(107008\theta^4+264320\theta^3+651536\theta^2+1298596\theta+1113327\right)-2^{28} x^{8}\left(704944\theta^4+3925888\theta^3+9920672\theta^2+12076292\theta+5776605\right)+2^{34} x^{9}\left(220796\theta^4+1480752\theta^3+4427225\theta^2+6675624\theta+4170854\right)-2^{36} 3 x^{10}\left(9216\theta^4-66432\theta^3-131864\theta^2+696808\theta+1370197\right)-2^{40} 3 x^{11}\left(168448\theta^4+1796608\theta^3+7226400\theta^2+13138336\theta+9227347\right)+2^{47} 3^{2} x^{12}\left(3584\theta^4+43776\theta^3+208688\theta^2+457392\theta+385875\right)-2^{52} 3^{2} x^{13}(4\theta+15)^2(4\theta+13)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 68/3, 1036/3, 44464/27, -8491132/81, ... --> OEIS Normalized instanton numbers (n0=1): 76/3, -3641/9, 746444/81, -69221068/243, 7315935712/729, ... ; Common denominator:...
\(-(-1+16z)(16z-3)^2(16z+1)^2(3072z^2-48z-1)^2(1024z^2-48z+1)^2\)
| \(-\frac{ 1}{ 16}\) | \(\frac{ 1}{ 128}-\frac{ 1}{ 384}\sqrt{ 57}\) | \(0\) | \(\frac{ 3}{ 128}-\frac{ 1}{ 128}\sqrt{ 7}I\) | \(\frac{ 3}{ 128}+\frac{ 1}{ 128}\sqrt{ 7}I\) | \(\frac{ 1}{ 128}+\frac{ 1}{ 384}\sqrt{ 57}\) | \(\frac{ 1}{ 16}\) | \(\frac{ 3}{ 16}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 13}{ 4}\) |
| \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(1\) | \(\frac{ 13}{ 4}\) |
| \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 2}\) | \(3\) | \(1\) | \(-2\) | \(\frac{ 15}{ 4}\) |
| \(1\) | \(4\) | \(0\) | \(1\) | \(1\) | \(4\) | \(2\) | \(3\) | \(\frac{ 15}{ 4}\) |