Atkin-Lehner |
37+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
121841d |
Isogeny class |
Conductor |
121841 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
503424 |
Modular degree for the optimal curve |
Δ |
-312610671398969 = -1 · 378 · 89 |
Discriminant |
Eigenvalues |
-1 1 -1 0 0 -4 3 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-352546,80544829] |
[a1,a2,a3,a4,a6] |
Generators |
[-663:5123:1] [315:722:1] |
Generators of the group modulo torsion |
j |
-1888690601881/121841 |
j-invariant |
L |
8.3184016301591 |
L(r)(E,1)/r! |
Ω |
0.51627616848831 |
Real period |
R |
8.0561549514219 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000009645 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
3293a1 |
Quadratic twists by: 37 |