New Number: 2.20 | AESZ: 133 | Superseeker: 12 -3284/3 | Hash: 4c9628f7dd48f4e9e6ec75303e557389
Degree: 2
\(\theta^4-2^{2} 3 x(2\theta+1)^2(3\theta^2+3\theta+1)+2^{4} 3^{3} x^{2}(2\theta+1)^2(2\theta+3)^2\)
Maple LaTex Coefficients of the holomorphic solution: 1, 12, 324, 8400, 44100, ... --> OEIS Normalized instanton numbers (n0=1): 12, -42, -3284/3, -20538, -103776, ... ; Common denominator:...
Discriminant
\(1-144z+6912z^2\)
Local exponents
Note:
Hadamard product A*f
Explicit solution not yet verified
Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, 12, -324, -29544, -1314756, -12971988, 2033927928, 146587697352,...
Coefficients of the q-coordinate : 0, 1, -36, 1134, -24912, 564597, -11502648, 173126610,...
| Gopakumar-Vafa invariants |
---|
g=0 | ,... |
g=1 | ,... |
g=2 | ,... |
Explicit solution
\(A_{n}=\dbinom{2n}{n}^2\sum_{k=0}^{n}(-1)^{k}3^{n-3k}\dbinom{n}{3k}\frac{(3k)!}{k!^3}\)
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 \(\frac{ 1}{ 6}+120\lambda\) | \(-\frac{ 5}{ 36}+20\lambda\) | \(-\frac{ 5}{ 54}+\frac{ 40}{ 3}\lambda\) | \(-.9896550e-2+\frac{ 50}{ 9}\lambda\) |
\(4+\frac{ 7}{ 1000000000}I\) | \(\frac{ 5}{ 3}-\frac{ 1}{ 500000000}I\) | \(\frac{ 4}{ 9}-\frac{ 1}{ 500000000}I\) | \(\frac{ 5}{ 54}-\frac{ 40}{ 3}\lambda\) |
\(-6.-.11e-7I\) | \(-1+\frac{ 3}{ 1000000000}I\) | \(\frac{ 1}{ 3}+\frac{ 3}{ 1000000000}I\) | \(-\frac{ 5}{ 36}+20\lambda\) |
\(36.000000031+.67e-7I\) | \(-24I3^{ \frac{ 19}{ 41}}\lambdaPi^3-\frac{ 1}{ 62500000}I\) | \(4-\frac{ 9}{ 500000000}I\) | \(\frac{ 11}{ 6}-120\lambda\) |
copy data \(\frac{ 11}{ 6}+120\lambda\) | \(-\frac{ 5}{ 36}-20\lambda\) | \(\frac{ 5}{ 54}+\frac{ 40}{ 3}\lambda\) | \(-.9896550e-2-\frac{ 50}{ 9}\lambda\) |
\(4\) | \(\frac{ 1}{ 3}\) | \(\frac{ 4}{ 9}\) | \(-\frac{ 5}{ 54}-\frac{ 40}{ 3}\lambda\) |
\(6\) | \(-1\) | \(\frac{ 5}{ 3}\) | \(-\frac{ 5}{ 36}-20\lambda\) |
\(36\) | \(-6\) | \(4\) | \(\frac{ 1}{ 6}-120\lambda\) |
copy data Basis of the Doran-Morgan lattice
\(\frac{ 5}{ 6}-120\lambda\) | \(\frac{ 78000000031}{ 6000000000}+\frac{ 71}{ 3000000000}I\) | \(\frac{ 302400000483599999147}{ 259200000446400001090}+\frac{ 1124400000899}{ 259200000446400001090}I\) | \(1\) |
\(-4-\frac{ 7}{ 1000000000}I\) | \(-\frac{ 48000000031}{ 2000000000}-\frac{ 89}{ 2000000000}I\) | \(-\frac{ 648000001115999998236}{ 648000001116000002725}-\frac{ 2412000002077}{ 648000001116000002725}I\) | \(0\) |
\(6+\frac{ 11}{ 1000000000}I\) | \(\frac{ 36000000031}{ 1000000000}+\frac{ 67}{ 1000000000}I\) | \(0\) | \(0\) |
\(-\frac{ 36000000031}{ 1000000000}-\frac{ 67}{ 1000000000}I\) | \(0\) | \(0\) | \(0\) |
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