Atkin-Lehner |
2+ 3- 13+ 73+ |
Signs for the Atkin-Lehner involutions |
Class |
68328c |
Isogeny class |
Conductor |
68328 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
46080 |
Modular degree for the optimal curve |
Δ |
8069400144 = 24 · 312 · 13 · 73 |
Discriminant |
Eigenvalues |
2+ 3- -2 0 0 13+ 4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2766,55825] |
[a1,a2,a3,a4,a6] |
Generators |
[-52:243:1] [33:22:1] |
Generators of the group modulo torsion |
j |
200647026688/691821 |
j-invariant |
L |
9.5138389165615 |
L(r)(E,1)/r! |
Ω |
1.3178324351835 |
Real period |
R |
3.6096542559477 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999888 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
22776g1 |
Quadratic twists by: -3 |