Atkin-Lehner |
2+ 3+ 7+ 19+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
23142c |
Isogeny class |
Conductor |
23142 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
49152 |
Modular degree for the optimal curve |
Δ |
1385445261312 = 216 · 33 · 72 · 19 · 292 |
Discriminant |
Eigenvalues |
2+ 3+ 0 7+ -6 0 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-9585,-360747] |
[a1,a2,a3,a4,a6] |
Generators |
[-482:647:8] [-53:70:1] |
Generators of the group modulo torsion |
j |
97402669215657625/1385445261312 |
j-invariant |
L |
4.8273693280491 |
L(r)(E,1)/r! |
Ω |
0.48291383802795 |
Real period |
R |
4.9981683562465 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999988 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69426bf1 |
Quadratic twists by: -3 |