Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696bj |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
675840 |
Modular degree for the optimal curve |
Δ |
-622150167634034688 = -1 · 214 · 311 · 118 |
Discriminant |
Eigenvalues |
2+ 3- 0 -1 11- -6 -4 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-319440,79178528] |
[a1,a2,a3,a4,a6] |
Generators |
[-503:10611:1] |
Generators of the group modulo torsion |
j |
-1408000/243 |
j-invariant |
L |
4.8293684241992 |
L(r)(E,1)/r! |
Ω |
0.27802637179878 |
Real period |
R |
4.3425452704794 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001047 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69696fk1 8712h1 23232f1 69696bi1 |
Quadratic twists by: -4 8 -3 -11 |