Atkin-Lehner |
5- 29+ 71- |
Signs for the Atkin-Lehner involutions |
Class |
51475d |
Isogeny class |
Conductor |
51475 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
24192 |
Modular degree for the optimal curve |
Δ |
15368118625 = 53 · 293 · 712 |
Discriminant |
Eigenvalues |
1 0 5- 0 2 -2 -2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-2422,-44889] |
[a1,a2,a3,a4,a6] |
Generators |
[10270:63973:125] |
Generators of the group modulo torsion |
j |
12572943815277/122944949 |
j-invariant |
L |
5.3942411004591 |
L(r)(E,1)/r! |
Ω |
0.68093242142771 |
Real period |
R |
7.9218450035492 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000032 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
51475e1 |
Quadratic twists by: 5 |