Atkin-Lehner |
2- 29+ 73+ |
Signs for the Atkin-Lehner involutions |
Class |
8468a |
Isogeny class |
Conductor |
8468 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
1488 |
Modular degree for the optimal curve |
Δ |
541952 = 28 · 29 · 73 |
Discriminant |
Eigenvalues |
2- 0 -4 2 -1 -6 -3 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-32,-60] |
[a1,a2,a3,a4,a6] |
Generators |
[-4:2:1] [-3:3:1] |
Generators of the group modulo torsion |
j |
14155776/2117 |
j-invariant |
L |
4.8078231502619 |
L(r)(E,1)/r! |
Ω |
2.0274086989625 |
Real period |
R |
0.79047096797693 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33872c1 76212k1 |
Quadratic twists by: -4 -3 |