Atkin-Lehner |
2+ 3+ 5+ 7+ |
Signs for the Atkin-Lehner involutions |
Class |
6720c |
Isogeny class |
Conductor |
6720 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
34002179850240000 = 220 · 32 · 54 · 78 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 7+ 4 2 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-7683201,-8194556799] |
[a1,a2,a3,a4,a6] |
Generators |
[-335512417313320:-14519567854631:209690452621] |
Generators of the group modulo torsion |
j |
191342053882402567201/129708022500 |
j-invariant |
L |
3.2776134934885 |
L(r)(E,1)/r! |
Ω |
0.090680523553492 |
Real period |
R |
18.072312361293 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
6720cd5 210e5 20160ce5 33600da6 |
Quadratic twists by: -4 8 -3 5 |