New Number: 2.16 | AESZ: 65 | Superseeker: 240 19105840 | Hash: 13ba368bcbb10731ac8727b510731ff2
Degree: 2
\(\theta^4-2^{4} 3 x(6\theta+1)(6\theta+5)(3\theta^2+3\theta+1)+2^{9} 3^{2} x^{2}(6\theta+1)(6\theta+5)(6\theta+7)(6\theta+11)\)
Maple LaTex Coefficients of the holomorphic solution: 1, 240, 277200, 457416960, 904864680720, ... --> OEIS Normalized instanton numbers (n0=1): 240, 57102, 19105840, 14810143935, 10017820614480, ... ; Common denominator:...
Discriminant
\((3456z-1)(1728z-1)\)
Local exponents
Note:
Hadamard product D*d
Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 240, 457056, 515857920, 947849668896, 1252227576810240, 1951472479155996672, 2805919645433093677056,...
Coefficients of the q-coordinate : 0, 1, -1488, 1737216, -1936036864, 2030351668656, -2106830943512064, 2118312344000340992,...
| Gopakumar-Vafa invariants |
---|
g=0 | ,... |
g=1 | ,... |
g=2 | ,... |
Explicit solution
\(A_{n}=\dbinom{3n}{n}\dbinom{6n}{3n}\sum_{k=0}^{n}\dbinom{n}{k}\dbinom{2k}{k}\dbinom{2n-2k}{n-k}\)
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 \(1.+2.277630552I\) | \(0\) | \(1.091364639I\) | \(.648450116\) |
\(\frac{ 23}{ 6}\) | \(1\) | \(\frac{ 529}{ 288}\) | \(-1.091364639I\) |
\(0\) | \(0\) | \(1\) | \(0\) |
\(8\) | \(0\) | \(\frac{ 23}{ 6}\) | \(1.-2.277630552I\) |
copy data \(\frac{ 37}{ 12}+940\lambda\) | \(-.52083333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333-1.138815272I\) | \(.99826388888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889+2.182729279I\) | \(1.025632871-1.186265914I\) |
\(\frac{ 23}{ 3}+\frac{ 1}{ 250000000}I\) | \(-\frac{ 11}{ 12}+\frac{ 3}{ 1000000000}I\) | \(\frac{ 529}{ 144}-\frac{ 1}{ 250000000}I\) | \(-.99826388888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889-2.182729279I\) |
\(4+\frac{ 1}{ 500000000}I\) | \(-1+\frac{ 1}{ 1000000000}I\) | \(\frac{ 35}{ 12}-\frac{ 1}{ 500000000}I\) | \(-\frac{ 25}{ 48}-235\lambda\) |
\(16+\frac{ 9}{ 1000000000}I\) | \(-3.999999988+.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8I\) | \(\frac{ 23}{ 3}-\frac{ 1}{ 125000000}I\) | \(-\frac{ 13}{ 12}-940\lambda\) |
copy data Basis of the Doran-Morgan lattice
\(-\frac{ 284703819}{ 125000000}I\) | \(\frac{ 31}{ 6}\) | \(1\) | \(1\) |
\(-\frac{ 23}{ 6}\) | \(-4\) | \(-1\) | \(0\) |
\(0\) | \(8\) | \(0\) | \(0\) |
\(-8\) | \(0\) | \(0\) | \(0\) |
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