Atkin-Lehner |
2- 3+ 5+ 7+ |
Signs for the Atkin-Lehner involutions |
Class |
6720bi |
Isogeny class |
Conductor |
6720 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
215040 |
Modular degree for the optimal curve |
Δ |
6405501887389080000 = 26 · 328 · 54 · 7 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7+ -4 6 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1600156,-768989294] |
[a1,a2,a3,a4,a6] |
j |
7079962908642659949376/100085966990454375 |
j-invariant |
L |
1.2091304721268 |
L(r)(E,1)/r! |
Ω |
0.13434783023632 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6720cb1 3360x3 20160et1 33600gy1 |
Quadratic twists by: -4 8 -3 5 |