New Number: 2.67 | AESZ: 245 | Superseeker: -6 -170 | Hash: 0ef0bca0dbecbedad92696fd7c0f9e42
Degree: 2
\(\theta^4-2 3 x\left(36\theta^4+66\theta^3+61\theta^2+28\theta+5\right)+2^{2} 3^{2} x^{2}(3\theta+2)^2(6\theta+7)^2\)
Maple LaTex Coefficients of the holomorphic solution: 1, 30, 1764, 127776, 10248750, ... --> OEIS Normalized instanton numbers (n0=1): -6, -33, -170, -1029, -3246, ... ; Common denominator:...
Discriminant
\((108z-1)^2\)
Local exponents
Note:
This is operator "2.67" from ...
Integral instantons: ,...
Coefficients of the Yukawa coupling: 1, -6, -270, -4596, -66126, -405756, 8587836, 424349304,...
Coefficients of the q-coordinate : 0, 1, -48, 1440, -32848, 637872, -11009952, 174295160,...
| 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 \(1.052168056+.90357723e-1I\) | \(\frac{ 1}{ 4}-\frac{ 1}{ 12}I\sqrt{ 3}\) | \(-33^{ \frac{ 1}{ 6}}Pi^{ \frac{ 9}{ 2}}Zeta(5)^6-6\lambda\) | \(.10688274e-1-\frac{ 1}{ 5}I5^{ \frac{ 4}{ 7}}ln(2)^12\) |
\(\frac{ 3}{ 2}-\frac{ 1}{ 2}I\sqrt{ 3}\) | \(\frac{ 3}{ 4}-\frac{ 1}{ 4}I\sqrt{ 3}\) | \(-\frac{ 1}{ 8}+\frac{ 1}{ 24}I\sqrt{ 3}\) | \(33^{ \frac{ 1}{ 6}}Pi^{ \frac{ 9}{ 2}}Zeta(5)^6+6\lambda\) |
\(0\) | \(\frac{ 9}{ 2}-\frac{ 3}{ 2}I\sqrt{ 3}\) | \(\frac{ 3}{ 4}-\frac{ 1}{ 4}I\sqrt{ 3}\) | \(\frac{ 1}{ 4}-\frac{ 1}{ 12}I\sqrt{ 3}\) |
\(-27+9I\sqrt{ 3}\) | \(0\) | \(\frac{ 3}{ 2}-\frac{ 1}{ 2}I\sqrt{ 3}\) | \(.447831944-.956383127I\) |
copy data Basis of the Doran-Morgan lattice
\(-\frac{ 6521007}{ 125000000}-\frac{ 90357723}{ 1000000000}I\) | \(-3+\frac{ 4511615154067544842086723740124334848694351954431101272196462779644508392806538050844596873167533211}{ 2604782223680891931509451724762066519358428478691519147090699072692122550847025398588836869330367971}I\) | \(\frac{ 1}{ 2}-\frac{ 3081490456277555159153769728602633601692409347626414678367139999430219011336903561652776870289659281}{ 3558198688874218386798087732443200684026390216561310209643580926168315471826781724716716871248950591}I\) | \(1\) |
\(-\frac{ 3}{ 2}+\frac{ 1}{ 2}I\sqrt{ 3}\) | \(\frac{ 27}{ 2}-\frac{ 5941739851857534525019677751646036095696294561235787866025785559858797774276172540036416876045407141}{ 762325578427705482137746574067229488156369299800529597635468373844463859062368874404292289563613477}I\) | \(-\frac{ 1}{ 2}+\frac{ 3081490456277555159153769728602633601692409347626414678367139999430219011336903561652776870289659281}{ 3558198688874218386798087732443200684026390216561310209643580926168315471826781724716716871248950591}I\) | \(0\) |
\(0\) | \(-27+\frac{ 11883479703715069050039355503292072191392589122471575732051571119717595548552345080072833752090814282}{ 762325578427705482137746574067229488156369299800529597635468373844463859062368874404292289563613477}I\) | \(0\) | \(0\) |
\(27-\frac{ 11883479703715069050039355503292072191392589122471575732051571119717595548552345080072833752090814282}{ 762325578427705482137746574067229488156369299800529597635468373844463859062368874404292289563613477}I\) | \(0\) | \(0\) | \(0\) |
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