New Number: 2.65 | AESZ: 183 | Superseeker: -4 -556/9 | Hash: 04a3788c3f9ed53281ae824deb33d833
Degree: 2
\(\theta^4+2^{2} x(2\theta+1)^2(7\theta^2+7\theta+3)+2^{4} 3 x^{2}(2\theta+1)(4\theta+3)(4\theta+5)(2\theta+3)\)
Maple LaTex Coefficients of the holomorphic solution: 1, -12, 324, -11280, 447300, ... --> OEIS Normalized instanton numbers (n0=1): -4, 8, -556/9, 624, -8928, ... ; Common denominator:...
Discriminant
\((48z+1)(64z+1)\)
Local exponents
Note:
This is operator "2.65" from ...
Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, -4, 60, -1672, 39996, -1116004, 28791288, -731576472,...
Coefficients of the q-coordinate : 0, 1, 28, 558, 9520, 144885, 2085960, 28114706,...
| Gopakumar-Vafa invariants |
---|
g=0 | ,... |
g=1 | ,... |
g=2 | ,... |
Explicit solution
\(A_{n}=\binom{2n}{n}\sum_{j,k=0}^{n}(-4)^{n-j}\binom{n}{j}\binom{n}{k}\binom{j}{k}\binom{2j}{j}\binom{2n-3k}{n}\)
Maple LaTex No topological data
Monodromy (with respect to Frobenius basis)
\(3.666666992+1.240581667I\) | \(-.888889273-.413527825I\) | \(.296296213+.137842738I\) | \(-.38694844e-1-.45947515e-1I\) |
\(16.000002509-.2845e-5I\) | \(-4.333336913-.1390e-5I\) | \(1.777778225+.1587e-5I\) | \(-.296296073-.137842774I\) |
\(48.000008758-.8909e-5I\) | \(-16.000011149-.4045e-5I\) | \(6.333334810+.4721e-5I\) | \(-.888888245-.413528325I\) |
\(144.000033661-.28975e-4I\) | \(-48.000035910-.11385e-4I\) | \(16.000005252+.13912e-4I\) | \(-1.666664890-1.240584998I\) |
copy data \(5.+.620290874I\) | \(-2-64\lambda\) | \(\frac{ 7}{ 9}+\frac{ 224}{ 9}\lambda\) | \(-.216878323-.68921208e-1I\) |
\(14\) | \(-6\) | \(\frac{ 49}{ 18}\) | \(-\frac{ 7}{ 9}-\frac{ 224}{ 9}\lambda\) |
\(36\) | \(-18\) | \(8\) | \(-2-64\lambda\) |
\(72\) | \(-36\) | \(14\) | \(-3.-.620290874I\) |
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 Basis of the Doran-Morgan lattice
\(-4-\frac{ 310145437}{ 500000000}I\) | \(8\) | \(\frac{ 1}{ 2}\) | \(1\) |
\(-14\) | \(0\) | \(-1\) | \(0\) |
\(-36\) | \(72\) | \(0\) | \(0\) |
\(-72\) | \(0\) | \(0\) | \(0\) |
copy data