Atkin-Lehner |
2- 3- 13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
84474bu |
Isogeny class |
Conductor |
84474 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
236800 |
Modular degree for the optimal curve |
Δ |
-11139260056938 = -1 · 2 · 37 · 135 · 193 |
Discriminant |
Eigenvalues |
2- 3- -2 -1 -3 13+ 4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-59576,-5584363] |
[a1,a2,a3,a4,a6] |
Generators |
[2430:15323:8] |
Generators of the group modulo torsion |
j |
-4676732925067/2227758 |
j-invariant |
L |
7.4680789526318 |
L(r)(E,1)/r! |
Ω |
0.15278822463144 |
Real period |
R |
6.1098286274147 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003149 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
28158g1 84474t1 |
Quadratic twists by: -3 -19 |