New Number: 2.10 | AESZ: 70 | Superseeker: 27 18089 | Hash: 3d2adae6eaf26a56c76b8b67d92cc5df
Degree: 2
\(\theta^4-3 x(3\theta+1)(3\theta+2)(10\theta^2+10\theta+3)+3^{4} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTex Coefficients of the holomorphic solution: 1, 18, 1350, 156240, 22141350, ... --> OEIS Normalized instanton numbers (n0=1): 27, 432, 18089, 997785, 68438142, ... ; Common denominator:...
Discriminant
\((243z-1)(27z-1)\)
Local exponents
Note:
Hadamard product $B\ast c$.
Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 27, 3483, 488430, 63861723, 8554767777, 1160441624934, 158655700035531,...
Coefficients of the q-coordinate : 0, 1, -69, 2196, -90131, 1380525, -161041824, -7106675719,...
| Gopakumar-Vafa invariants |
|---|
| g=0 | ,... |
| g=1 | ,... |
| g=2 | ,... |
Explicit solution
\(A_{n}=\dbinom{2n}{n}\dbinom{3n}{n}\sum_{k=0}^{n}\dbinom{n}{k}^{2}\dbinom{2k}{k}\)
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 | \(1.+.755979502I\) | \(0\) | \(26\lambda\) | \(.31750278e-1\) |
| \(3\) | \(1\) | \(\frac{ 1}{ 2}\) | \(-26\lambda\) |
| \(0\) | \(0\) | \(1\) | \(0\) |
| \(18\) | \(0\) | \(3\) | \(1.-.755979502I\) |
copy data | \(4+468\lambda\) | \(-1.-.755979502I\) | \(\frac{ 1}{ 2}+78\lambda\) | \(-.71415832e-1-52\lambda\) |
| \(9\) | \(-2\) | \(\frac{ 3}{ 2}\) | \(-\frac{ 1}{ 2}-78\lambda\) |
| \(18\) | \(-6\) | \(4\) | \(-1.-.755979502I\) |
| \(54\) | \(-18\) | \(9\) | \(-2-468\lambda\) |
copy data Basis of the Doran-Morgan lattice
| \(-\frac{ 377989751}{ 500000000}I\) | \(6\) | \(1\) | \(1\) |
| \(-3\) | \(-9\) | \(-1\) | \(0\) |
| \(0\) | \(18\) | \(0\) | \(0\) |
| \(-18\) | \(0\) | \(0\) | \(0\) |
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