Atkin-Lehner |
2- 3- 5+ 7+ |
Signs for the Atkin-Lehner involutions |
Class |
6720bw |
Isogeny class |
Conductor |
6720 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
1585446912000 = 226 · 33 · 53 · 7 |
Discriminant |
Eigenvalues |
2- 3- 5+ 7+ 0 -2 -6 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-31841,-2196705] |
[a1,a2,a3,a4,a6] |
Generators |
[3991:251904:1] |
Generators of the group modulo torsion |
j |
13619385906841/6048000 |
j-invariant |
L |
4.4167159092651 |
L(r)(E,1)/r! |
Ω |
0.35740721725944 |
Real period |
R |
4.1192191017033 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6720f1 1680m1 20160en1 33600ey1 |
Quadratic twists by: -4 8 -3 5 |