New Number: 2.12 | AESZ: 64 | Superseeker: 432 78259376 | Hash: 43991f21e20c16ab91690259b788b4cd
Degree: 2
\(\theta^4-2^{2} 3 x(6\theta+1)(6\theta+5)(10\theta^2+10\theta+3)+2^{4} 3^{4} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)\)
Maple LaTex Coefficients of the holomorphic solution: 1, 180, 207900, 379819440, 855338063580, ... --> OEIS Normalized instanton numbers (n0=1): 432, 130842, 78259376, 68104755558, 73096116588720, ... ; Common denominator:...
Discriminant
\((3888z-1)(432z-1)\)
Local exponents
Note:
Hadamard product $B\ast c$.
Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 432, 1047168, 2113003584, 4358705402880, 9137014573590432, 19430849236761091584, 41639311772154039173760,...
Coefficients of the q-coordinate : 0, 1, -1176, 761004, -577776704, 287718512334, -296784707487264, 8781941004951992,...
| Gopakumar-Vafa invariants |
|---|
| g=0 | ,... |
| g=1 | ,... |
| g=2 | ,... |
Explicit solution
\(A_{n}=\dbinom{3n}{n}\dbinom{6n}{3n}\sum_{k=0}^{n}\dbinom{n}{k}^2\dbinom{2k}{k}\)
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 | \(1+364\lambda\) | \(0\) | \(182\lambda\) | \(.518587877\) |
| \(3\) | \(1\) | \(\frac{ 3}{ 2}\) | \(-182\lambda\) |
| \(0\) | \(0\) | \(1\) | \(0\) |
| \(6\) | \(0\) | \(3\) | \(1-364\lambda\) |
copy data | \(4.+5.291856516I\) | \(-1-364\lambda\) | \(\frac{ 3}{ 2}+546\lambda\) | \(1.055763632-364\lambda\) |
| \(9\) | \(-2\) | \(\frac{ 9}{ 2}\) | \(-\frac{ 3}{ 2}-546\lambda\) |
| \(6\) | \(-2\) | \(4\) | \(-1-364\lambda\) |
| \(18\) | \(-6\) | \(9\) | \(-2.-5.291856516I\) |
copy data Basis of the Doran-Morgan lattice
| \(-364\lambda\) | \(4\) | \(1\) | \(1\) |
| \(-3\) | \(-3\) | \(-1\) | \(0\) |
| \(0\) | \(6\) | \(0\) | \(0\) |
| \(-6\) | \(0\) | \(0\) | \(0\) |
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