Atkin-Lehner |
2- 5+ 13+ 67+ |
Signs for the Atkin-Lehner involutions |
Class |
69680o |
Isogeny class |
Conductor |
69680 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
6912 |
Modular degree for the optimal curve |
Δ |
-905840 = -1 · 24 · 5 · 132 · 67 |
Discriminant |
Eigenvalues |
2- -1 5+ 1 -2 13+ 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-66,235] |
[a1,a2,a3,a4,a6] |
Generators |
[1:13:1] [9:17:1] |
Generators of the group modulo torsion |
j |
-2017433344/56615 |
j-invariant |
L |
8.3017392839902 |
L(r)(E,1)/r! |
Ω |
2.7914040137169 |
Real period |
R |
1.487018583339 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999782 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17420b1 |
Quadratic twists by: -4 |