New Number: 2.17 | AESZ: 111 | Superseeker: 32 1440 | Hash: d8535e0f3d0bfd4ebcc9c042df43c218
Degree: 2
\(\theta^4-2^{4} x(2\theta+1)^2(8\theta^2+8\theta+3)+2^{12} x^{2}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTex Coefficients of the holomorphic solution: 1, 48, 5904, 940800, 169520400, ... --> OEIS Normalized instanton numbers (n0=1): 32, -96, 1440, 19704, -14496, ... ; Common denominator:...
Discriminant
\((256z-1)^2\)
Local exponents
Note:
B-Incarnations:
Fibre product 81111- x 18--21, 4*11-- x 53211,
Double Octics: D.O.8, D.O.36, D.O.73, D.O.249, D.O.258,D.O.265
Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 32, -736, 38912, 1260320, -1811968, 3421042688, 56010539008,...
Coefficients of the q-coordinate : 0, 1, -128, 11616, -870400, 57668144, -3495272448, 197815529984,...
| Gopakumar-Vafa invariants |
---|
g=0 | ,... |
g=1 | ,... |
g=2 | ,... |
Explicit solution
\(A_{n}=\dbinom{2n}{n}^2\sum_{k=0}^{n}4^{n-k}\dbinom{2k}{k}^2\dbinom{2n-2k}{n-k}\)
Maple LaTex No topological data
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 \(-\frac{ 2}{ 3}+96\lambda\) | \(48\lambda\) | \(-\frac{ 5}{ 72}+4\lambda\) | \(-.13526746e-1\) |
\(-\frac{ 2}{ 3}\) | \(\frac{ 2}{ 3}\) | \(-\frac{ 1}{ 36}\) | \(-\frac{ 5}{ 72}-4\lambda\) |
\(-8\) | \(0\) | \(\frac{ 2}{ 3}\) | \(-48\lambda\) |
\(-16\) | \(-8\) | \(-\frac{ 2}{ 3}\) | \(-\frac{ 2}{ 3}-96\lambda\) |
copy data Basis of the Doran-Morgan lattice
\(\frac{ 5}{ 3}-96\lambda\) | \(\frac{ 2}{ 3}\) | \(\frac{ 1}{ 2}\) | \(1\) |
\(\frac{ 2}{ 3}\) | \(0\) | \(-1\) | \(0\) |
\(8\) | \(-16\) | \(0\) | \(0\) |
\(16\) | \(0\) | \(0\) | \(0\) |
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