Atkin-Lehner |
2+ 5- 13- 79- |
Signs for the Atkin-Lehner involutions |
Class |
51350o |
Isogeny class |
Conductor |
51350 |
Conductor |
∏ cp |
54 |
Product of Tamagawa factors cp |
deg |
414720 |
Modular degree for the optimal curve |
Δ |
-1692510442187500 = -1 · 22 · 58 · 133 · 793 |
Discriminant |
Eigenvalues |
2+ -2 5- -1 0 13- 0 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-244951,46683798] |
[a1,a2,a3,a4,a6] |
Generators |
[277:-464:1] [278:49311:8] |
Generators of the group modulo torsion |
j |
-4161010187744905/4332826732 |
j-invariant |
L |
5.2619110460945 |
L(r)(E,1)/r! |
Ω |
0.47047929622719 |
Real period |
R |
1.8640250089254 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999997 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
51350s1 |
Quadratic twists by: 5 |