Atkin-Lehner |
3- 5+ 7- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
68355l |
Isogeny class |
Conductor |
68355 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
3612672 |
Modular degree for the optimal curve |
Δ |
128243132520890625 = 38 · 56 · 79 · 31 |
Discriminant |
Eigenvalues |
1 3- 5+ 7- 4 -2 2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-31148280,66919047075] |
[a1,a2,a3,a4,a6] |
Generators |
[102420:9260415:64] |
Generators of the group modulo torsion |
j |
113609864431873783/4359375 |
j-invariant |
L |
6.3403553023327 |
L(r)(E,1)/r! |
Ω |
0.24393689256769 |
Real period |
R |
6.4979462883602 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999995511 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
22785r1 68355bf1 |
Quadratic twists by: -3 -7 |