New Number: 2.4 | AESZ: 62 | Superseeker: 372 71562236 | Hash: 07a3fd7577f878056e765831c6820f3d
Degree: 2
\(\theta^4-2^{2} 3 x(6\theta+1)(6\theta+5)(7\theta^2+7\theta+2)-2^{7} 3^{2} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)\)
Maple LaTex Coefficients of the holomorphic solution: 1, 120, 138600, 228708480, 463140798120, ... --> OEIS Normalized instanton numbers (n0=1): 372, 136182, 71562236, 63364481358, 65860679690400, ... ; Common denominator:...
Discriminant
\(-(432z+1)(3456z-1)\)
Local exponents
Note:
Hadamard product D*a
Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 372, 1089828, 1932180744, 4055327896740, 8232584961300372, 17221930420090297320, 36109212055335698287128,...
Coefficients of the q-coordinate : 0, 1, -804, 60894, 33466160, -125049218259, -73798244967672, -137218105849556206,...
| Gopakumar-Vafa invariants |
---|
g=0 | ,... |
g=1 | ,... |
g=2 | ,... |
Explicit solution
\(A_{n}=\frac{(6n)!}{(3n)!(2n)!n!}\sum_{k=0}^{n}\dbinom{n}{k}^3\)
Maple LaTex Characteristic classes:
Monodromy (with respect to Frobenius basis)
\(4.+3.547288434I\) | \(-\frac{ 3}{ 2}-366\lambda\) | \(1.7500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+2.069251586I\) | \(.298604603-366\lambda\) |
\(7\) | \(-\frac{ 5}{ 2}\) | \(\frac{ 49}{ 12}\) | \(-1.7500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-2.069251586I\) |
\(6\) | \(-3\) | \(\frac{ 9}{ 2}\) | \(-\frac{ 3}{ 2}-366\lambda\) |
\(12\) | \(-6\) | \(7\) | \(-2.-3.547288434I\) |
copy data \(1\) | \(-1\) | \(\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 6}\) |
\(0\) | \(1\) | \(-1\) | \(\frac{ 1}{ 2}\) |
\(0\) | \(0\) | \(1\) | \(-1\) |
\(0\) | \(0\) | \(0\) | \(1\) |
copy data \(1+366\lambda\) | \(0\) | \(183\lambda\) | \(.524302301\) |
\(3\) | \(1\) | \(\frac{ 3}{ 2}\) | \(-183\lambda\) |
\(0\) | \(0\) | \(1\) | \(0\) |
\(6\) | \(0\) | \(3\) | \(1-366\lambda\) |
copy data Basis of the Doran-Morgan lattice
\(-366\lambda\) | \(4\) | \(1\) | \(1\) |
\(-3\) | \(-3\) | \(-1\) | \(0\) |
\(0\) | \(6\) | \(0\) | \(0\) |
\(-6\) | \(0\) | \(0\) | \(0\) |
copy data