Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696cq |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
245760 |
Modular degree for the optimal curve |
Δ |
8182741051584 = 26 · 38 · 117 |
Discriminant |
Eigenvalues |
2+ 3- -2 0 11- -6 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-144111,-21056420] |
[a1,a2,a3,a4,a6] |
Generators |
[-1507764:90040:6859] |
Generators of the group modulo torsion |
j |
4004529472/99 |
j-invariant |
L |
4.5994065061296 |
L(r)(E,1)/r! |
Ω |
0.24503375531003 |
Real period |
R |
9.3852508193369 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001201 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696cr1 34848t4 23232bx1 6336bc1 |
Quadratic twists by: -4 8 -3 -11 |