New Number: 2.11 | AESZ: 69 | Superseeker: 64 246848 | Hash: 729adc350de26d9415643078ed8d3867
Degree: 2
\(\theta^4-2^{2} x(4\theta+1)(4\theta+3)(10\theta^2+10\theta+3)+2^{4} 3^{2} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)\)
Maple LaTex Coefficients of the holomorphic solution: 1, 36, 6300, 1718640, 575675100, ... --> OEIS Normalized instanton numbers (n0=1): 64, 2616, 246848, 32024824, 5160268864, ... ; Common denominator:...
Discriminant
\((576z-1)(64z-1)\)
Local exponents
Note:
Hadamard product $C\ast c$
Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 64, 20992, 6664960, 2049609728, 645033608064, 205583909214208, 66049430635281920,...
Coefficients of the q-coordinate : 0, 1, -168, 14124, -1462208, 78268110, -14975497440, -813107957064,...
| Gopakumar-Vafa invariants |
---|
g=0 | ,... |
g=1 | ,... |
g=2 | ,... |
Explicit solution
\(A_n=\dbinom{2n}{n}\dbinom{4n}{2n}\sum_{k=0}^{n}\dbinom{n}{k}^2\dbinom{2k}{k}\)
Maple LaTex Characteristic classes:
Monodromy (with respect to Frobenius basis)
\(1\) | \(-1\) | \(\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 6}\) |
\(0\) | \(1\) | \(-1\) | \(\frac{ 1}{ 2}\) |
\(0\) | \(0\) | \(1\) | \(-1\) |
\(0\) | \(0\) | \(0\) | \(1\) |
copy data \(1+224\lambda\) | \(0\) | \(56\lambda\) | \(.98194154e-1\) |
\(3\) | \(1\) | \(\frac{ 3}{ 4}\) | \(-56\lambda\) |
\(0\) | \(0\) | \(1\) | \(0\) |
\(12\) | \(0\) | \(3\) | \(1-224\lambda\) |
copy data \(4.+3.256527087I\) | \(-1-224\lambda\) | \(\frac{ 3}{ 4}+168\lambda\) | \(.44582463e-1-112\lambda\) |
\(9\) | \(-2\) | \(\frac{ 9}{ 4}\) | \(-\frac{ 3}{ 4}-168\lambda\) |
\(12\) | \(-4\) | \(4\) | \(-1-224\lambda\) |
\(36\) | \(-12\) | \(9\) | \(-2.-3.256527087I\) |
copy data Basis of the Doran-Morgan lattice
\(-224\lambda\) | \(5\) | \(1\) | \(1\) |
\(-3\) | \(-6\) | \(-1\) | \(0\) |
\(0\) | \(12\) | \(0\) | \(0\) |
\(-12\) | \(0\) | \(0\) | \(0\) |
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