Atkin-Lehner |
2- 3+ 7+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
56784be |
Isogeny class |
Conductor |
56784 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
48384 |
Modular degree for the optimal curve |
Δ |
176882614272 = 215 · 33 · 7 · 134 |
Discriminant |
Eigenvalues |
2- 3+ 0 7+ -3 13+ 3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1408,2560] |
[a1,a2,a3,a4,a6] |
Generators |
[48:208:1] [-27:142:1] |
Generators of the group modulo torsion |
j |
2640625/1512 |
j-invariant |
L |
8.2973084501832 |
L(r)(E,1)/r! |
Ω |
0.86832347557777 |
Real period |
R |
0.79629583939149 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7098ba1 56784bu1 |
Quadratic twists by: -4 13 |