1
New Number: 5.33 | AESZ: 216 | Superseeker: 9 14201/3 | Hash: af7027bf24acce4fd0ed5b09e575e2a5
Degree: 5
\(\theta^4-3 x\theta(2+11\theta+18\theta^2+27\theta^3)-2 3^{3} x^{2}\left(72\theta^4+414\theta^3+603\theta^2+330\theta+64\right)+2^{2} 3^{5} x^{3}\left(93\theta^4-720\theta^2-708\theta-184\right)+2^{3} 3^{7} x^{4}(2\theta+1)(54\theta^3+405\theta^2+544\theta+200)-2^{4} 3^{10} x^{5}(2\theta+1)(3\theta+2)(3\theta+4)(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 216, 7200, 567000, ... --> OEIS Normalized instanton numbers (n0=1): 9, 225, 14201/3, 154800, 6298596, ... ; Common denominator:...
\(-(27z+1)(108z-1)(36z+1)(-1+18z)^2\)
\(-\frac{ 1}{ 27}\) | \(-\frac{ 1}{ 36}\) | \(0\) | \(\frac{ 1}{ 108}\) | \(\frac{ 1}{ 18}\) | \(\infty\) |
---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 2}{ 3}\) |
\(1\) | \(1\) | \(0\) | \(1\) | \(3\) | \(\frac{ 4}{ 3}\) |
\(2\) | \(2\) | \(0\) | \(2\) | \(4\) | \(\frac{ 3}{ 2}\) |
2
New Number: 5.38 | AESZ: 223 | Superseeker: 18 64744/3 | Hash: e3ab25cffe4a0968b175bd9e98c96427
Degree: 5
\(\theta^4+2 3 x\theta(48\theta^3-12\theta^2-7\theta-1)+2^{2} 3^{3} x^{2}\left(392\theta^4+488\theta^3+775\theta^2+376\theta+64\right)+2^{4} 3^{5} x^{3}\left(1184\theta^4+3288\theta^3+3512\theta^2+1635\theta+278\right)+2^{6} 3^{8} x^{4}(169\theta^2+361\theta+238)(2\theta+1)^2+2^{11} 3^{11} x^{5}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, -432, 7200, 1587600, ... --> OEIS Normalized instanton numbers (n0=1): 18, -873, 64744/3, -229968, -1628892, ... ; Common denominator:...
\((36z+1)(13824z^2+36z+1)(1+108z)^2\)
\(-\frac{ 1}{ 36}\) | \(-\frac{ 1}{ 108}\) | \(-\frac{ 1}{ 768}-\frac{ 5}{ 2304}\sqrt{ 15}I\) | \(-\frac{ 1}{ 768}+\frac{ 5}{ 2304}\sqrt{ 15}I\) | \(0\) | \(\infty\) |
---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(3\) | \(1\) | \(1\) | \(0\) | \(\frac{ 3}{ 2}\) |
\(2\) | \(4\) | \(2\) | \(2\) | \(0\) | \(\frac{ 3}{ 2}\) |
3
New Number: 5.74 | AESZ: 297 | Superseeker: 26/7 55644/7 | Hash: cd0b6008fa6b70d89e004100b5698063
Degree: 5
\(7^{2} \theta^4-2 7 x\theta(520\theta^3+68\theta^2+41\theta+7)-2^{2} 3 x^{2}\left(9480\theta^4+153912\theta^3+212893\theta^2+108080\theta+18816\right)+2^{4} 3^{3} 7 x^{3}\left(13424\theta^4+48792\theta^3+45656\theta^2+17979\theta+2606\right)-2^{6} 3^{7} x^{4}(2\theta+1)^2(2257\theta^2+3601\theta+1942)+2^{11} 3^{11} x^{5}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 288, 7200, 1058400, ... --> OEIS Normalized instanton numbers (n0=1): 26/7, 2594/7, 55644/7, 2996576/7, 135364470/7, ... ; Common denominator:...
\((128z-1)(432z^2-72z-1)(-7+324z)^2\)
\(\frac{ 1}{ 12}-\frac{ 1}{ 18}\sqrt{ 3}\) | \(0\) | \(\frac{ 1}{ 128}\) | \(\frac{ 7}{ 324}\) | \(\frac{ 1}{ 12}+\frac{ 1}{ 18}\sqrt{ 3}\) | \(\infty\) |
---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) |
\(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(\frac{ 3}{ 2}\) |
\(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |