New Number: 2.18 | AESZ: 110 | Superseeker: 36 8076 | Hash: 5060b638cac581d5f0f9dd7f40d90e6c
Degree: 2
\(\theta^4-2^{2} 3 x(3\theta+1)(3\theta+2)(8\theta^2+8\theta+3)+2^{8} 3^{2} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTex Coefficients of the holomorphic solution: 1, 72, 14760, 3951360, 1198751400, ... --> OEIS Normalized instanton numbers (n0=1): 36, -144, 8076, -57996, 6960672, ... ; Common denominator:...
Discriminant
\((432z-1)^2\)
Local exponents
Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 36, -1116, 218088, -3712860, 870084036, -2622855960, 3444157244088,...
Coefficients of the q-coordinate : 0, 1, -228, 39006, -5773648, 784430637, -100616704632, 12381829002386,...
| Gopakumar-Vafa invariants |
---|
g=0 | ,... |
g=1 | ,... |
g=2 | ,... |
Explicit solution
\(A_{n}=\dbinom{2n}{n}\dbinom{3n}{n}\sum_{k=0}^{n}4^{n-k}\dbinom{2k}{k}^2\dbinom{2n-2k}{n-k}\)
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 \(-\frac{ 1}{ 2}+24\lambda\) | \(12\lambda\) | \(-\frac{ 1}{ 8}+2\lambda\) | \(-.1127229e-2\) |
\(-1\) | \(\frac{ 1}{ 2}\) | \(-\frac{ 1}{ 12}\) | \(-\frac{ 1}{ 8}-2\lambda\) |
\(-6\) | \(0\) | \(\frac{ 1}{ 2}\) | \(-12\lambda\) |
\(-12\) | \(-6\) | \(-1\) | \(-\frac{ 1}{ 2}-24\lambda\) |
copy data Basis of the Doran-Morgan lattice
\(\frac{ 3}{ 2}-24\lambda\) | \(0\) | \(\frac{ 1}{ 2}\) | \(1\) |
\(1\) | \(0\) | \(-1\) | \(0\) |
\(6\) | \(-12\) | \(0\) | \(0\) |
\(12\) | \(0\) | \(0\) | \(0\) |
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