New Number: 2.25 | AESZ: 138 | Superseeker: 27 2618 | Hash: c524254b716132352b27914640b03c8b
Degree: 2
\(\theta^4-3 x(3\theta+1)(3\theta+2)(17\theta^2+17\theta+6)+2^{3} 3^{4} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTex Coefficients of the holomorphic solution: 1, 36, 3780, 524160, 82952100, ... --> OEIS Normalized instanton numbers (n0=1): 27, 189/4, 2618, 43713, 2319057, ... ; Common denominator:...
Discriminant
\((243z-1)(216z-1)\)
Local exponents
Note:
Hadamard product $B\ast g$.
Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 27, 405, 70713, 2798037, 289882152, 21198969351, 1788576309540,...
Coefficients of the q-coordinate : 0, 1, -120, 10782, -841288, 60234693, -4078954368, 264886454966,...
| Gopakumar-Vafa invariants |
---|
g=0 | ,... |
g=1 | ,... |
g=2 | ,... |
Explicit solution
\(A_{n}=\dbinom{2n}{n}\dbinom{3n}{n}\sum_{j,k}^{n}(-1)^{j}8^{n-j}\dbinom{n}{j}\dbinom{j}{k}^3\)
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 \(1.+.755979502I\) | \(0\) | \(\frac{ 39}{ 2}\lambda\) | \(.15875139e-1\) |
\(\frac{ 9}{ 2}\) | \(1\) | \(\frac{ 9}{ 16}\) | \(-\frac{ 39}{ 2}\lambda\) |
\(0\) | \(0\) | \(1\) | \(0\) |
\(36\) | \(0\) | \(\frac{ 9}{ 2}\) | \(1.-.755979502I\) |
copy data \(.84386396e-1+.881341465I\) | \(-.593907697+1.816219110I\) | \(.987405021+.251865740I\) | \(-.18197034e-1-.280246794I\) |
\(-.610146073+4.105015738I\) | \(3.086102688+5.881005017I\) | \(\frac{ 1}{ ln}(2)^{ \frac{ 8}{ 3}}ln(3)^{ \frac{ 8}{ 5}}Zeta(5)^8-1.317777791I\) | \(-.605925748-.688412508I\) |
\(-1.084750363+4.722447485I\) | \(1.891556916+7.035664131I\) | \(4.676916900-1.255046419I\) | \(-.642466556-.856579334I\) |
\(-4.881168587+32.840125900I\) | \(16.688821505+47.048040140I\) | \(24.445126799-10.542222328I\) | \(-3.847405984-5.507300063I\) |
copy data Basis of the Doran-Morgan lattice
\(-\frac{ 377989751}{ 500000000}I\) | \(\frac{ 21}{ 2}\) | \(1\) | \(1\) |
\(-\frac{ 9}{ 2}\) | \(-18\) | \(-1\) | \(0\) |
\(0\) | \(36\) | \(0\) | \(0\) |
\(-36\) | \(0\) | \(0\) | \(0\) |
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