Atkin-Lehner |
2+ 3+ 7- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
42042s |
Isogeny class |
Conductor |
42042 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
501760 |
Modular degree for the optimal curve |
Δ |
67190090713733988 = 22 · 37 · 79 · 114 · 13 |
Discriminant |
Eigenvalues |
2+ 3+ 2 7- 11- 13+ 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-175494,-25473888] |
[a1,a2,a3,a4,a6] |
Generators |
[616:9724:1] |
Generators of the group modulo torsion |
j |
14812625308879/1665033084 |
j-invariant |
L |
4.3267191997989 |
L(r)(E,1)/r! |
Ω |
0.23496149990963 |
Real period |
R |
4.6036469820226 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999993 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
126126ev1 42042br1 |
Quadratic twists by: -3 -7 |