Atkin-Lehner |
2+ 23- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
69184a |
Isogeny class |
Conductor |
69184 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
17920 |
Modular degree for the optimal curve |
Δ |
-832421888 = -1 · 214 · 23 · 472 |
Discriminant |
Eigenvalues |
2+ 0 0 2 0 -6 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-220,1872] |
[a1,a2,a3,a4,a6] |
Generators |
[-16:36:1] [-2:48:1] |
Generators of the group modulo torsion |
j |
-71874000/50807 |
j-invariant |
L |
10.387923751577 |
L(r)(E,1)/r! |
Ω |
1.4607201226682 |
Real period |
R |
3.5557543126701 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000014 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69184c1 8648a1 |
Quadratic twists by: -4 8 |