Atkin-Lehner |
2+ 3- 7- 11- 23- |
Signs for the Atkin-Lehner involutions |
Class |
85008z |
Isogeny class |
Conductor |
85008 |
Conductor |
∏ cp |
84 |
Product of Tamagawa factors cp |
deg |
225792 |
Modular degree for the optimal curve |
Δ |
-36945956534256 = -1 · 24 · 37 · 73 · 11 · 234 |
Discriminant |
Eigenvalues |
2+ 3- -3 7- 11- 1 -2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-19152,-1067661] |
[a1,a2,a3,a4,a6] |
Generators |
[189:1449:1] |
Generators of the group modulo torsion |
j |
-48558896031486208/2309122283391 |
j-invariant |
L |
6.4557831673563 |
L(r)(E,1)/r! |
Ω |
0.20235349595542 |
Real period |
R |
0.37980347760967 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000596 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
42504c1 |
Quadratic twists by: -4 |