New Number: 2.1 | AESZ: 45 | Superseeker: 12 3204 | Hash: cdf289f6febf84eb577a238542a57457
Degree: 2
\(\theta^4-2^{2} x(2\theta+1)^2(7\theta^2+7\theta+2)-2^{7} x^{2}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTex Coefficients of the holomorphic solution: 1, 8, 360, 22400, 1695400, ... --> OEIS Normalized instanton numbers (n0=1): 12, 163, 3204, 107582, 4203360, ... ; Common denominator:...
Discriminant
\(-(16z+1)(128z-1)\)
Local exponents
Note:
Hadamard product $A \ast a$, where $A$ is (:case 2.1.1)
Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 12, 1316, 86520, 6886564, 525420012, 41230582760, 3244416959208,...
Coefficients of the q-coordinate : 0, 1, -28, -34, 1488, -200915, -6984840, -407799534,...
| Gopakumar-Vafa invariants |
---|
g=0 | ,... |
g=1 | ,... |
g=2 | ,... |
Explicit solution
\(A_{n}=\dbinom{2n}{n}^2\sum_{k=0}^{n}\dbinom{n}{k}^3\)
Maple LaTex Characteristic classes:
Monodromy (with respect to Frobenius basis)
\(4+240\lambda\) | \(-\frac{ 3}{ 2}-120\lambda\) | \(\frac{ 5}{ 8}+50\lambda\) | \(-.159319280-30\lambda\) |
\(10\) | \(-4\) | \(\frac{ 25}{ 12}\) | \(-\frac{ 5}{ 8}-50\lambda\) |
\(24\) | \(-12\) | \(6\) | \(-\frac{ 3}{ 2}-120\lambda\) |
\(48\) | \(-24\) | \(10\) | \(-2-240\lambda\) |
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 \(1+120\lambda\) | \(0\) | \(15\lambda\) | \(.14090360e-1\) |
\(3\) | \(1\) | \(\frac{ 3}{ 8}\) | \(-15\lambda\) |
\(0\) | \(0\) | \(1\) | \(0\) |
\(24\) | \(0\) | \(3\) | \(1-120\lambda\) |
copy data Basis of the Doran-Morgan lattice
\(-120\lambda\) | \(7\) | \(1\) | \(1\) |
\(-3\) | \(-12\) | \(-1\) | \(0\) |
\(0\) | \(24\) | \(0\) | \(0\) |
\(-24\) | \(0\) | \(0\) | \(0\) |
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