Atkin-Lehner |
2+ 3- 5+ 7- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
49350bb |
Isogeny class |
Conductor |
49350 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
688128 |
Modular degree for the optimal curve |
Δ |
-574338868992000000 = -1 · 214 · 32 · 56 · 74 · 473 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 7- 2 0 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-102726,-38610152] |
[a1,a2,a3,a4,a6] |
Generators |
[59105:509329:125] |
Generators of the group modulo torsion |
j |
-7672532588448337/36757687615488 |
j-invariant |
L |
5.7071575376944 |
L(r)(E,1)/r! |
Ω |
0.12062834359393 |
Real period |
R |
5.9139889594689 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999762 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
1974e1 |
Quadratic twists by: 5 |