New Number: 2.3 | AESZ: 68 | Superseeker: 52 220220 | Hash: 13a48045ff0a42a9fcfbdb710baf1997
Degree: 2
\(\theta^4-2^{2} x(4\theta+1)(4\theta+3)(7\theta^2+7\theta+2)-2^{7} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)\)
Maple LaTex Coefficients of the holomorphic solution: 1, 24, 4200, 1034880, 311711400, ... --> OEIS Normalized instanton numbers (n0=1): 52, 2814, 220220, 29135058, 4512922272, ... ; Common denominator:...
Discriminant
\(-(64z+1)(512z-1)\)
Local exponents
Note:
C*a
Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 52, 22564, 5945992, 1864666276, 564115284052, 175701961097704, 54872373731039896,...
Coefficients of the q-coordinate : 0, 1, -116, 478, 113008, -56372435, -6168706136, -1532666623214,...
| Gopakumar-Vafa invariants |
---|
g=0 | ,... |
g=1 | ,... |
g=2 | ,... |
Explicit solution
\(A_{n}=\dbinom{2n}{n}\dbinom{4n}{2n}\sum_{k=0}^{n}\dbinom{n}{k}^3\)
Maple LaTex Characteristic classes:
Monodromy (with respect to Frobenius basis)
\(4.+2.209786237I\) | \(-1.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-1.104893119I\) | \(1+152\lambda\) | \(-.171535199-114\lambda\) |
\(8\) | \(-3\) | \(\frac{ 8}{ 3}\) | \(-1-152\lambda\) |
\(12\) | \(-6\) | \(5\) | \(-1.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-1.104893119I\) |
\(24\) | \(-12\) | \(8\) | \(-2.-2.209786237I\) |
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 \(1.+1.104893119I\) | \(0\) | \(57\lambda\) | \(\frac{ 276}{ 2713}\) |
\(3\) | \(1\) | \(\frac{ 3}{ 4}\) | \(-57\lambda\) |
\(0\) | \(0\) | \(1\) | \(0\) |
\(12\) | \(0\) | \(3\) | \(1.-1.104893119I\) |
copy data Basis of the Doran-Morgan lattice
\(-\frac{ 1104893119}{ 1000000000}I\) | \(5\) | \(1\) | \(1\) |
\(-3\) | \(-6\) | \(-1\) | \(0\) |
\(0\) | \(12\) | \(0\) | \(0\) |
\(-12\) | \(0\) | \(0\) | \(0\) |
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