New Number: 2.22 | AESZ: 135 | Superseeker: 36 -206716/3 | Hash: 85e55291bd94bb32087b43f104c60645
Degree: 2
\(\theta^4-2^{2} 3 x(4\theta+1)(4\theta+3)(3\theta^2+3\theta+1)+2^{4} 3^{3} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)\)
Maple LaTex Coefficients of the holomorphic solution: 1, 36, 3780, 388080, 8108100, ... --> OEIS Normalized instanton numbers (n0=1): 36, -477, -206716/3, -4431924, -27005472, ... ; Common denominator:...
Discriminant
\(1-576z+110592z^2\)
Local exponents
Integral instantons: Hadamard, product, $C, \ast, f$.,...
Coefficients of the Yukawa coupling: 1, 36, -3780, -1860408, -283646916, -3375683964, 8182006866936, 1873126855818072,...
Coefficients of the q-coordinate : 0, 1, -156, 22446, -2570800, 297228021, -32847734088, 3343576302482,...
| Gopakumar-Vafa invariants |
---|
g=0 | ,... |
g=1 | ,... |
g=2 | ,... |
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 \(\frac{ 5}{ 24}+Itan(\frac{ 801}{ 812})\) | \(-\frac{ 19}{ 144}+52\lambda\) | \(-\frac{ 323}{ 1728}+\frac{ 221}{ 3}\lambda\) | \(.92182440e-1+\frac{ 247}{ 9}\lambda\) |
\(\frac{ 17}{ 4}+\frac{ 9}{ 1000000000}I\) | \(\frac{ 41}{ 24}-\frac{ 3}{ 1000000000}I\) | \(\frac{ 289}{ 288}-\frac{ 1}{ 250000000}I\) | \(\frac{ 323}{ 1728}-\frac{ 221}{ 3}\lambda\) |
\(-3-\frac{ 3}{ 500000000}I\) | \(-\frac{ 1}{ 2}+\frac{ 1}{ 500000000}I\) | \(\frac{ 7}{ 24}+\frac{ 3}{ 1000000000}I\) | \(-\frac{ 19}{ 144}+52\lambda\) |
\(18.000000018+.41e-7I\) | \(3.000000039-.12000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7I\) | \(\frac{ 17}{ 4}-\frac{ 9}{ 500000000}I\) | \(\frac{ 43}{ 24}-Itan(\frac{ 801}{ 812})\) |
copy data \(\frac{ 43}{ 24}+Itan(\frac{ 801}{ 812})\) | \(-\frac{ 19}{ 144}-52\lambda\) | \(\frac{ 323}{ 1728}+\frac{ 221}{ 3}\lambda\) | \(.92182440e-1-\frac{ 247}{ 9}\lambda\) |
\(\frac{ 17}{ 4}\) | \(\frac{ 7}{ 24}\) | \(\frac{ 289}{ 288}\) | \(-\frac{ 323}{ 1728}-\frac{ 221}{ 3}\lambda\) |
\(3\) | \(-\frac{ 1}{ 2}\) | \(\frac{ 41}{ 24}\) | \(-\frac{ 19}{ 144}-52\lambda\) |
\(18\) | \(-3\) | \(\frac{ 17}{ 4}\) | \(\frac{ 5}{ 24}-Itan(\frac{ 801}{ 812})\) |
copy data Basis of the Doran-Morgan lattice
\(\frac{ 19}{ 24}-\frac{ 1162393719353719131361189363784404603456366390101814206736549803033200099854000208071729302850101578}{ 768799759549186043811713254203741173211443985818991590275710787225120378790852066470688698366857287}I\) | \(\frac{ 8750000003}{ 1000000000}+\frac{ 113}{ 6000000000}I\) | \(\frac{ 378000000701999998397}{ 324000000648000002005}+\frac{ 1707000001584}{ 324000000648000002005}I\) | \(1\) |
\(-\frac{ 17}{ 4}-\frac{ 9}{ 1000000000}I\) | \(-\frac{ 12000000009}{ 1000000000}-\frac{ 53}{ 2000000000}I\) | \(-\frac{ 324000000647999998643}{ 324000000648000002005}-\frac{ 1476000001476}{ 324000000648000002005}I\) | \(0\) |
\(3+\frac{ 3}{ 500000000}I\) | \(\frac{ 9000000009}{ 500000000}+\frac{ 41}{ 1000000000}I\) | \(0\) | \(0\) |
\(-\frac{ 9000000009}{ 500000000}-\frac{ 41}{ 1000000000}I\) | \(0\) | \(0\) | \(0\) |
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