Atkin-Lehner |
3- 5+ 29- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
69165m |
Isogeny class |
Conductor |
69165 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
184320 |
Modular degree for the optimal curve |
Δ |
8224972115625 = 310 · 55 · 292 · 53 |
Discriminant |
Eigenvalues |
-1 3- 5+ 0 0 6 0 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-31838,2190156] |
[a1,a2,a3,a4,a6] |
Generators |
[26:1161:1] |
Generators of the group modulo torsion |
j |
4895766888629401/11282540625 |
j-invariant |
L |
3.9633939372251 |
L(r)(E,1)/r! |
Ω |
0.73838454510582 |
Real period |
R |
2.6838277993998 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999990429 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23055d1 |
Quadratic twists by: -3 |