Atkin-Lehner |
2+ 3- 13+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
51714d |
Isogeny class |
Conductor |
51714 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
172032 |
Modular degree for the optimal curve |
Δ |
-597229341067008 = -1 · 28 · 37 · 137 · 17 |
Discriminant |
Eigenvalues |
2+ 3- -2 0 0 13+ 17+ 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,12897,-1035059] |
[a1,a2,a3,a4,a6] |
Generators |
[75:554:1] [78:625:1] |
Generators of the group modulo torsion |
j |
67419143/169728 |
j-invariant |
L |
6.7116677916795 |
L(r)(E,1)/r! |
Ω |
0.26600530330761 |
Real period |
R |
6.3078326900102 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
17238l1 3978j1 |
Quadratic twists by: -3 13 |