Atkin-Lehner |
2- 3+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
69696dy |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
405504 |
Modular degree for the optimal curve |
Δ |
-2970335001724992 = -1 · 26 · 39 · 119 |
Discriminant |
Eigenvalues |
2- 3+ 4 0 11+ 4 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,35937,0] |
[a1,a2,a3,a4,a6] |
j |
1728 |
j-invariant |
L |
4.3091513346867 |
L(r)(E,1)/r! |
Ω |
0.26932195799495 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
16 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696dy1 34848bh2 69696ea1 69696dz1 |
Quadratic twists by: -4 8 -3 -11 |