1
New Number: 5.12 | AESZ: 74 | Superseeker: -30 -14632 | Hash: e668180adb7c88d4e5fbab5eb7ee61c7
Degree: 5
\(\theta^4-2 3 x\left(99\theta^4+36\theta^3+39\theta^2+21\theta+4\right)+2^{2} 3^{2} x^{2}\left(3807\theta^4+3564\theta^3+3798\theta^2+1683\theta+284\right)-2^{3} 3^{5} x^{3}\left(7857\theta^4+13608\theta^3+14562\theta^2+7317\theta+1444\right)+2^{4} 3^{9} x^{4}\left(2592\theta^4+7128\theta^3+8550\theta^2+4851\theta+1052\right)-2^{5} 3^{13} x^{5}(3\theta+2)(3\theta+4)(6\theta+5)(6\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 24, 1152, 71520, 5101200, ... --> OEIS Normalized instanton numbers (n0=1): -30, -516, -14632, -4227807/8, -22139868, ... ; Common denominator:...
\(-(-1+54z)(162z-1)^2(108z-1)^2\)
\(0\) | \(\frac{ 1}{ 108}\) | \(\frac{ 1}{ 54}\) | \(\frac{ 1}{ 162}\) | \(\infty\) |
---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
\(0\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(\frac{ 5}{ 6}\) |
\(0\) | \(\frac{ 1}{ 2}\) | \(1\) | \(3\) | \(\frac{ 7}{ 6}\) |
\(0\) | \(1\) | \(2\) | \(4\) | \(\frac{ 4}{ 3}\) |
2
New Number: 5.65 | AESZ: 273 | Superseeker: 63/5 14016/5 | Hash: cf49bc645cb0404ce7bc9ca1d41d3152
Degree: 5
\(5^{2} \theta^4-3 5 x\left(333\theta^4+882\theta^3+781\theta^2+340\theta+60\right)+2^{2} 3^{2} x^{2}\left(5184\theta^4+40662\theta^3+71829\theta^2+47700\theta+11540\right)+2^{2} 3^{5} x^{3}\left(8424\theta^4+9720\theta^3-46899\theta^2-63045\theta-21260\right)-2^{4} 3^{8} x^{4}\left(1296\theta^4+12312\theta^3+23094\theta^2+16263\theta+3956\right)-2^{6} 3^{11} x^{5}(3\theta+2)(3\theta+4)(6\theta+5)(6\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 36, 2196, 161280, 13032900, ... --> OEIS Normalized instanton numbers (n0=1): 63/5, -747/4, 14016/5, -55584, 6071598/5, ... ; Common denominator:...
\(-(-1+27z)(108z+5)^2(108z-1)^2\)
\(0\) | \(\frac{ 1}{ 108}\) | \(\infty\) | \(-\frac{ 5}{ 108}\) | \(\frac{ 1}{ 27}\) |
---|---|---|---|---|
\(0\) | \(0\) | \(\frac{ 2}{ 3}\) | \(0\) | \(0\) |
\(0\) | \(\frac{ 1}{ 6}\) | \(\frac{ 5}{ 6}\) | \(1\) | \(1\) |
\(0\) | \(\frac{ 5}{ 6}\) | \(\frac{ 7}{ 6}\) | \(3\) | \(1\) |
\(0\) | \(1\) | \(\frac{ 4}{ 3}\) | \(4\) | \(2\) |
3
New Number: 8.21 | AESZ: 251 | Superseeker: -9 -3145/3 | Hash: dd2b60d18804c72129ba319fc8b50023
Degree: 8
\(\theta^4-3 x\theta(-2-11\theta-18\theta^2+27\theta^3)-2 3^{2} x^{2}\left(39\theta^4+480\theta^3+474\theta^2+276\theta+64\right)+2^{3} 3^{4} x^{3}\left(348\theta^4+1152\theta^3+1759\theta^2+1110\theta+260\right)-2^{3} 3^{5} x^{4}\left(3420\theta^4+15912\theta^3+28437\theta^2+20544\theta+5296\right)+2^{4} 3^{7} x^{5}\left(1125\theta^4+12546\theta^3+31089\theta^2+26448\theta+7480\right)+2^{5} 3^{9} x^{6}\left(1395\theta^4+3240\theta^3-3378\theta^2-7146\theta-2696\right)-2^{7} 3^{11} x^{7}\left(351\theta^4+2646\theta^3+4767\theta^2+3309\theta+800\right)-2^{7} 3^{13} x^{8}(3\theta+2)(3\theta+4)(6\theta+5)(6\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 72, -1440, 48600, ... --> OEIS Normalized instanton numbers (n0=1): -9, -27/4, -3145/3, -20907/4, -327348, ... ; Common denominator:...
\(-(54z+1)(27z-1)(432z^2-36z+1)(-1+36z+324z^2)^2\)
\(0\) | \(\frac{ 1}{ 27}\) | \(\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I\) | \(-\frac{ 1}{ 54}\) | \(\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I\) | \(\infty\) | \(-\frac{ 1}{ 18}+\frac{ 1}{ 18}\sqrt{ 2}\) | \(-\frac{ 1}{ 18}-\frac{ 1}{ 18}\sqrt{ 2}\) |
---|---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) | \(0\) | \(0\) |
\(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 5}{ 6}\) | \(1\) | \(1\) |
\(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 6}\) | \(3\) | \(3\) |
\(0\) | \(2\) | \(2\) | \(2\) | \(2\) | \(\frac{ 4}{ 3}\) | \(4\) | \(4\) |