Atkin-Lehner |
2- 3+ 7- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
84084m |
Isogeny class |
Conductor |
84084 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
317952 |
Modular degree for the optimal curve |
Δ |
212419523364048 = 24 · 36 · 73 · 11 · 136 |
Discriminant |
Eigenvalues |
2- 3+ 2 7- 11- 13+ -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-23837,-1222878] |
[a1,a2,a3,a4,a6] |
j |
272949697970176/38706181371 |
j-invariant |
L |
0.77570293763519 |
L(r)(E,1)/r! |
Ω |
0.38785148896382 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
84084z1 |
Quadratic twists by: -7 |