Atkin-Lehner |
2+ 3+ 5- 71+ |
Signs for the Atkin-Lehner involutions |
Class |
68160k |
Isogeny class |
Conductor |
68160 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
36864 |
Modular degree for the optimal curve |
Δ |
5807232000 = 210 · 32 · 53 · 712 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -2 0 -4 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1405,-19475] |
[a1,a2,a3,a4,a6] |
Generators |
[-23:12:1] [-20:15:1] |
Generators of the group modulo torsion |
j |
299751798784/5671125 |
j-invariant |
L |
8.95873351698 |
L(r)(E,1)/r! |
Ω |
0.78064525819633 |
Real period |
R |
1.9126770285869 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000017 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68160dl1 8520h1 |
Quadratic twists by: -4 8 |