Atkin-Lehner |
2- 3- 5- 7- 67- |
Signs for the Atkin-Lehner involutions |
Class |
84420bb |
Isogeny class |
Conductor |
84420 |
Conductor |
∏ cp |
672 |
Product of Tamagawa factors cp |
deg |
1548288 |
Modular degree for the optimal curve |
Δ |
-754205826543750000 = -1 · 24 · 37 · 58 · 77 · 67 |
Discriminant |
Eigenvalues |
2- 3- 5- 7- -3 -5 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1167897,487590689] |
[a1,a2,a3,a4,a6] |
Generators |
[-1247:2205:1] [223:-15435:1] |
Generators of the group modulo torsion |
j |
-15103925323442662144/64660993359375 |
j-invariant |
L |
11.668777064064 |
L(r)(E,1)/r! |
Ω |
0.28571515592079 |
Real period |
R |
0.060774695437794 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000219 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
28140d1 |
Quadratic twists by: -3 |