New Number: 2.21 | AESZ: 134 | Superseeker: 18 -5177 | Hash: cc6d92c4b8a8dadb92b447c54e3a2a2f
Degree: 2
\(\theta^4-3^{2} x(3\theta+1)(3\theta+2)(3\theta^2+3\theta+1)+3^{5} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)
Maple LaTex Coefficients of the holomorphic solution: 1, 18, 810, 35280, 311850, ... --> OEIS Normalized instanton numbers (n0=1): 18, -207/2, -5177, -155979, -923301, ... ; Common denominator:...
Discriminant
\(1-243z+19683z^2\)
Local exponents
Note:
Hadamard product $B\ast f$
Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 18, -810, -139761, -9983466, -115412607, 46702921761, 5144778419274,...
Coefficients of the q-coordinate : 0, 1, -63, 3564, -150735, 6501681, -261382950, 9012994434,...
| Gopakumar-Vafa invariants |
---|
g=0 | ,... |
g=1 | ,... |
g=2 | ,... |
Explicit solution
\(A_{n}=\dbinom{2n}{n}\dbinom{3n}{n}\sum_{k=0}^{n}(-1)^{k}3^{n-3k}\dbinom{n}{3k}\frac{(3k)!}{k!^3}\)
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 \(\frac{ 3}{ 16}+198\lambda\) | \(-\frac{ 13}{ 96}+33\lambda\) | \(-\frac{ 143}{ 1152}+\frac{ 121}{ 4}\lambda\) | \(.9648440e-2+.57748434e-1I\) |
\(\frac{ 33}{ 8}+\frac{ 1}{ 125000000}I\) | \(\frac{ 27}{ 16}-\frac{ 1}{ 500000000}I\) | \(\frac{ 121}{ 192}-\frac{ 3}{ 1000000000}I\) | \(\frac{ 143}{ 1152}-\frac{ 121}{ 4}\lambda\) |
\(-\frac{ 9}{ 2}-\frac{ 9}{ 1000000000}I\) | \(-\frac{ 3}{ 4}+\frac{ 1}{ 500000000}I\) | \(\frac{ 5}{ 16}+\frac{ 3}{ 1000000000}I\) | \(-\frac{ 13}{ 96}+33\lambda\) |
\(27.000000025+.54000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7I\) | \(4.500000045-.14000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7I\) | \(\frac{ 33}{ 8}-\frac{ 9}{ 500000000}I\) | \(\frac{ 29}{ 16}-198\lambda\) |
copy data \(\frac{ 29}{ 16}+198\lambda\) | \(-\frac{ 13}{ 96}-33\lambda\) | \(\frac{ 143}{ 1152}+\frac{ 121}{ 4}\lambda\) | \(.9648440e-2-.57748434e-1I\) |
\(\frac{ 33}{ 8}\) | \(\frac{ 5}{ 16}\) | \(\frac{ 121}{ 192}\) | \(-\frac{ 143}{ 1152}-\frac{ 121}{ 4}\lambda\) |
\(\frac{ 9}{ 2}\) | \(-\frac{ 3}{ 4}\) | \(\frac{ 27}{ 16}\) | \(-\frac{ 13}{ 96}-33\lambda\) |
\(27\) | \(-\frac{ 9}{ 2}\) | \(\frac{ 33}{ 8}\) | \(\frac{ 3}{ 16}-198\lambda\) |
copy data Basis of the Doran-Morgan lattice
\(\frac{ 13}{ 16}-198\lambda\) | \(\frac{ 2610000001}{ 240000000}+\frac{ 43}{ 2000000000}I\) | \(\frac{ 850500001462499997223}{ 729000001350000003541}+\frac{ 3402000002925}{ 729000001350000003541}I\) | \(1\) |
\(-\frac{ 33}{ 8}-\frac{ 1}{ 125000000}I\) | \(-\frac{ 1440000001}{ 80000000}-\frac{ 9}{ 250000000}I\) | \(-\frac{ 729000001349999997709}{ 729000001350000003541}-\frac{ 2916000002700}{ 729000001350000003541}I\) | \(0\) |
\(\frac{ 9}{ 2}+\frac{ 9}{ 1000000000}I\) | \(\frac{ 1080000001}{ 40000000}+\frac{ 27}{ 500000000}I\) | \(0\) | \(0\) |
\(-\frac{ 1080000001}{ 40000000}-\frac{ 27}{ 500000000}I\) | \(0\) | \(0\) | \(0\) |
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