New Number: 2.9 | AESZ: 58 | Superseeker: 16 11056/3 | Hash: 1ca6d3d1c4514db0651efce420265f5a
Degree: 2
\(\theta^4-2^{2} x(2\theta+1)^2(10\theta^2+10\theta+3)+2^{4} 3^{2} x^{2}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTex Coefficients of the holomorphic solution: 1, 12, 540, 37200, 3131100, ... --> OEIS Normalized instanton numbers (n0=1): 16, 142, 11056/3, 121470, 4971792, ... ; Common denominator:...
Discriminant
\((144z-1)(16z-1)\)
Local exponents
Note:
Hadamard product A*c
Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 16, 1152, 99520, 7775232, 621474016, 50322249216, 4106002362240,...
Coefficients of the q-coordinate : 0, 1, -40, 684, -15808, 79566, -10214112, -374227528,...
| Gopakumar-Vafa invariants |
|---|
| g=0 | ,... |
| g=1 | ,... |
| g=2 | ,... |
Explicit solution
\(A_{n}=\dbinom{2n}{n}^2\sum_{k=0}^{n}\dbinom{n}{k}^2\dbinom{2k}{k}\)
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 | \(1+112\lambda\) | \(0\) | \(14\lambda\) | \(.12274269e-1\) |
| \(3\) | \(1\) | \(\frac{ 3}{ 8}\) | \(-14\lambda\) |
| \(0\) | \(0\) | \(1\) | \(0\) |
| \(24\) | \(0\) | \(3\) | \(1-112\lambda\) |
copy data | \(4.+1.628263543I\) | \(-1-112\lambda\) | \(\frac{ 3}{ 8}+42\lambda\) | \(-.88177192e-1-28\lambda\) |
| \(9\) | \(-2\) | \(\frac{ 9}{ 8}\) | \(-\frac{ 3}{ 8}-42\lambda\) |
| \(24\) | \(-8\) | \(4\) | \(-1-112\lambda\) |
| \(72\) | \(-24\) | \(9\) | \(-2.-1.628263543I\) |
copy data Basis of the Doran-Morgan lattice
| \(-112\lambda\) | \(7\) | \(1\) | \(1\) |
| \(-3\) | \(-12\) | \(-1\) | \(0\) |
| \(0\) | \(24\) | \(0\) | \(0\) |
| \(-24\) | \(0\) | \(0\) | \(0\) |
copy data