Atkin-Lehner |
2- 3- 7+ |
Signs for the Atkin-Lehner involutions |
Class |
672f |
Isogeny class |
Conductor |
672 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
64 |
Modular degree for the optimal curve |
Δ |
28224 = 26 · 32 · 72 |
Discriminant |
Eigenvalues |
2- 3- -2 7+ -4 -6 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-14,-24] |
[a1,a2,a3,a4,a6] |
Generators |
[6:12:1] |
Generators of the group modulo torsion |
j |
5088448/441 |
j-invariant |
L |
2.2099943157884 |
L(r)(E,1)/r! |
Ω |
2.4672111687199 |
Real period |
R |
1.7914918218655 |
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 |
672e1 1344k2 2016c1 16800k1 |
Quadratic twists by: -4 8 -3 5 |