Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696ck |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
3686400 |
Modular degree for the optimal curve |
Δ |
4.3053788012653E+21 |
Discriminant |
Eigenvalues |
2+ 3- 2 4 11- -2 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-5667519,-4123528508] |
[a1,a2,a3,a4,a6] |
Generators |
[7645699197519328:148342526387780274:2672309557133] |
Generators of the group modulo torsion |
j |
243578556889408/52089208083 |
j-invariant |
L |
8.9564521138483 |
L(r)(E,1)/r! |
Ω |
0.099330442678329 |
Real period |
R |
22.542062313979 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999996965 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696cn1 34848cf3 23232cf1 6336bb1 |
Quadratic twists by: -4 8 -3 -11 |