Atkin-Lehner |
2+ 3- 11+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
6138f |
Isogeny class |
Conductor |
6138 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
86016 |
Modular degree for the optimal curve |
Δ |
133646529356955648 = 216 · 313 · 113 · 312 |
Discriminant |
Eigenvalues |
2+ 3- 2 -2 11+ -4 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-569601,-164384451] |
[a1,a2,a3,a4,a6] |
Generators |
[557445:36372252:125] |
Generators of the group modulo torsion |
j |
28035534600833657617/183328572506112 |
j-invariant |
L |
3.0942601797541 |
L(r)(E,1)/r! |
Ω |
0.17385129814965 |
Real period |
R |
8.8991575348799 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
49104bn1 2046j1 67518cb1 |
Quadratic twists by: -4 -3 -11 |