Atkin-Lehner |
2- 3- 5+ 7+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
84420i |
Isogeny class |
Conductor |
84420 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
172032 |
Modular degree for the optimal curve |
Δ |
-7477374870000 = -1 · 24 · 313 · 54 · 7 · 67 |
Discriminant |
Eigenvalues |
2- 3- 5+ 7+ -1 5 6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1713,-134363] |
[a1,a2,a3,a4,a6] |
j |
-47659369216/641064375 |
j-invariant |
L |
1.2696278446106 |
L(r)(E,1)/r! |
Ω |
0.31740697920784 |
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 |
28140q1 |
Quadratic twists by: -3 |