Atkin-Lehner |
2- 3- 7- 59- |
Signs for the Atkin-Lehner involutions |
Class |
69384bc |
Isogeny class |
Conductor |
69384 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
9984 |
Modular degree for the optimal curve |
Δ |
-416304 = -1 · 24 · 32 · 72 · 59 |
Discriminant |
Eigenvalues |
2- 3- -1 7- 0 4 5 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-51,-162] |
[a1,a2,a3,a4,a6] |
Generators |
[11:27:1] |
Generators of the group modulo torsion |
j |
-19081216/531 |
j-invariant |
L |
8.5246997342557 |
L(r)(E,1)/r! |
Ω |
0.89034227427796 |
Real period |
R |
2.3936580291984 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000018 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69384q1 |
Quadratic twists by: -7 |