Atkin-Lehner |
2- 19- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
67868c |
Isogeny class |
Conductor |
67868 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
157680 |
Modular degree for the optimal curve |
Δ |
-31593002743216 = -1 · 24 · 197 · 472 |
Discriminant |
Eigenvalues |
2- 2 -2 4 -4 4 -2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-3369,281834] |
[a1,a2,a3,a4,a6] |
Generators |
[579:12635:27] |
Generators of the group modulo torsion |
j |
-5619712/41971 |
j-invariant |
L |
9.0263617035336 |
L(r)(E,1)/r! |
Ω |
0.56546654002365 |
Real period |
R |
2.6604467475048 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000179 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
3572a1 |
Quadratic twists by: -19 |