Atkin-Lehner |
2- 3+ 7+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
49728cr |
Isogeny class |
Conductor |
49728 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
16708608 = 210 · 32 · 72 · 37 |
Discriminant |
Eigenvalues |
2- 3+ 0 7+ -4 -4 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-453,3861] |
[a1,a2,a3,a4,a6] |
Generators |
[-15:84:1] [-3:72:1] |
Generators of the group modulo torsion |
j |
10061824000/16317 |
j-invariant |
L |
7.7198006319446 |
L(r)(E,1)/r! |
Ω |
2.1954078414331 |
Real period |
R |
1.7581700507423 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
49728cc1 12432bq1 |
Quadratic twists by: -4 8 |