Atkin-Lehner |
3+ 23- 41- |
Signs for the Atkin-Lehner involutions |
Class |
8487d |
Isogeny class |
Conductor |
8487 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1120 |
Modular degree for the optimal curve |
Δ |
-585603 = -1 · 33 · 232 · 41 |
Discriminant |
Eigenvalues |
2 3+ 0 2 -3 4 -1 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,15,29] |
[a1,a2,a3,a4,a6] |
Generators |
[18:65:8] |
Generators of the group modulo torsion |
j |
13824000/21689 |
j-invariant |
L |
8.6017077418887 |
L(r)(E,1)/r! |
Ω |
1.9776724765577 |
Real period |
R |
1.087352410959 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8487a1 |
Quadratic twists by: -3 |