Atkin-Lehner |
3- 5- 13- 31- |
Signs for the Atkin-Lehner involutions |
Class |
78585x |
Isogeny class |
Conductor |
78585 |
Conductor |
∏ cp |
42 |
Product of Tamagawa factors cp |
deg |
1415232 |
Modular degree for the optimal curve |
Δ |
-693434841812578125 = -1 · 33 · 57 · 139 · 31 |
Discriminant |
Eigenvalues |
-1 3- 5- 0 -3 13- 0 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-1648345,-815676850] |
[a1,a2,a3,a4,a6] |
Generators |
[1535:15710:1] |
Generators of the group modulo torsion |
j |
-46706562254197/65390625 |
j-invariant |
L |
4.9551049744785 |
L(r)(E,1)/r! |
Ω |
0.066614853882824 |
Real period |
R |
1.7710567987803 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999664 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
78585m1 |
Quadratic twists by: 13 |