Atkin-Lehner |
2+ 3+ 13- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
51168c |
Isogeny class |
Conductor |
51168 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
211200 |
Modular degree for the optimal curve |
Δ |
1499093970776064 = 212 · 35 · 13 · 415 |
Discriminant |
Eigenvalues |
2+ 3+ 1 -2 -3 13- 7 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-59105,-5187951] |
[a1,a2,a3,a4,a6] |
j |
5574985947090496/365989738959 |
j-invariant |
L |
1.2298139422518 |
L(r)(E,1)/r! |
Ω |
0.30745348556852 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51168q1 102336w1 |
Quadratic twists by: -4 8 |