New Number: 2.13 | AESZ: 36 | Superseeker: 16 1232 | Hash: dea6fdf568a5907a24ba30fef2caf124
Degree: 2
\(\theta^4-2^{4} x(2\theta+1)^2(3\theta^2+3\theta+1)+2^{9} x^{2}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTex Coefficients of the holomorphic solution: 1, 16, 720, 44800, 3312400, ... --> OEIS Normalized instanton numbers (n0=1): 16, 42, 1232, 32159, 990128, ... ; Common denominator:...
Discriminant
\((128z-1)(64z-1)\)
Local exponents
Note:
A*d
Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 16, 352, 33280, 2058528, 123766016, 7347718144, 439489011712,...
Coefficients of the q-coordinate : 0, 1, -48, 1536, -44032, 1041840, -25188864, 473850880,...
| Gopakumar-Vafa invariants |
---|
g=0 | ,... |
g=1 | ,... |
g=2 | ,... |
Explicit solution
\(A_{n}=\dbinom{2n}{n}^2\sum_{k=0}^{n}\dbinom{n}{k}\dbinom{2k}{k}\dbinom{2n-2k}{n-k}\)
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 \(1+88\lambda\) | \(0\) | \(\frac{ 55}{ 6}\lambda\) | \(.5683112e-2\) |
\(\frac{ 10}{ 3}\) | \(1\) | \(\frac{ 25}{ 72}\) | \(-\frac{ 55}{ 6}\lambda\) |
\(0\) | \(0\) | \(1\) | \(0\) |
\(32\) | \(0\) | \(\frac{ 10}{ 3}\) | \(1-88\lambda\) |
copy data \(\frac{ 10}{ 3}+176\lambda\) | \(-\frac{ 7}{ 12}-44\lambda\) | \(\frac{ 35}{ 144}+\frac{ 55}{ 3}\lambda\) | \(-.73703221e-1-\frac{ 77}{ 6}\lambda\) |
\(\frac{ 20}{ 3}+\frac{ 1}{ 500000000}I\) | \(-\frac{ 2}{ 3}+\frac{ 1}{ 1000000000}I\) | \(\frac{ 25}{ 36}\) | \(-\frac{ 35}{ 144}-\frac{ 55}{ 3}\lambda\) |
\(16+\frac{ 1}{ 200000000}I\) | \(-4+\frac{ 1}{ 500000000}I\) | \(\frac{ 8}{ 3}-\frac{ 1}{ 500000000}I\) | \(-\frac{ 7}{ 12}-44\lambda\) |
\(64.+.23e-7I\) | \(-15.999999981+.90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8I\) | \(\frac{ 20}{ 3}-\frac{ 1}{ 125000000}I\) | \(-\frac{ 4}{ 3}-176\lambda\) |
copy data Basis of the Doran-Morgan lattice
\(-88\lambda\) | \(\frac{ 26}{ 3}\) | \(1\) | \(1\) |
\(-\frac{ 10}{ 3}\) | \(-16\) | \(-1\) | \(0\) |
\(0\) | \(32\) | \(0\) | \(0\) |
\(-32\) | \(0\) | \(0\) | \(0\) |
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