Atkin-Lehner |
2+ 5+ 7+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
67270b |
Isogeny class |
Conductor |
67270 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
25088 |
Modular degree for the optimal curve |
Δ |
133463680 = 27 · 5 · 7 · 313 |
Discriminant |
Eigenvalues |
2+ -1 5+ 7+ -3 -3 4 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-128,-128] |
[a1,a2,a3,a4,a6] |
Generators |
[-66:203:8] [-3:17:1] |
Generators of the group modulo torsion |
j |
7880599/4480 |
j-invariant |
L |
5.3528230977067 |
L(r)(E,1)/r! |
Ω |
1.5319553892048 |
Real period |
R |
1.7470558005124 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000063 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
67270a1 |
Quadratic twists by: -31 |