Atkin-Lehner |
2+ 3+ 5+ 7+ |
Signs for the Atkin-Lehner involutions |
Class |
117600f |
Isogeny class |
Conductor |
117600 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
2128896 |
Modular degree for the optimal curve |
Δ |
-168101597160000000 = -1 · 29 · 36 · 57 · 78 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 7+ 3 1 -4 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-4479008,3650101512] |
[a1,a2,a3,a4,a6] |
Generators |
[-163:66150:1] |
Generators of the group modulo torsion |
j |
-215474070728/3645 |
j-invariant |
L |
5.8050974358186 |
L(r)(E,1)/r! |
Ω |
0.2955668065138 |
Real period |
R |
1.6367132748802 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000078892 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117600gj1 23520bv1 117600da1 |
Quadratic twists by: -4 5 -7 |