Atkin-Lehner |
2- 5+ 7- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
8470v |
Isogeny class |
Conductor |
8470 |
Conductor |
∏ cp |
168 |
Product of Tamagawa factors cp |
deg |
40320 |
Modular degree for the optimal curve |
Δ |
612748220170240 = 228 · 5 · 73 · 113 |
Discriminant |
Eigenvalues |
2- 0 5+ 7- 11+ -4 4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-60468,5612951] |
[a1,a2,a3,a4,a6] |
Generators |
[-27:2701:1] |
Generators of the group modulo torsion |
j |
18370278334948779/460366807040 |
j-invariant |
L |
5.9166955476237 |
L(r)(E,1)/r! |
Ω |
0.51320868006952 |
Real period |
R |
0.27449594869628 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
67760w1 76230ce1 42350a1 59290dv1 |
Quadratic twists by: -4 -3 5 -7 |