Atkin-Lehner |
3- 11+ 17- 31- |
Signs for the Atkin-Lehner involutions |
Class |
52173j |
Isogeny class |
Conductor |
52173 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
32256 |
Modular degree for the optimal curve |
Δ |
12183595479 = 37 · 11 · 17 · 313 |
Discriminant |
Eigenvalues |
-1 3- -3 0 11+ -1 17- 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-1094,13142] |
[a1,a2,a3,a4,a6] |
Generators |
[-234:1229:8] [-6:142:1] |
Generators of the group modulo torsion |
j |
198461344537/16712751 |
j-invariant |
L |
5.2688099848505 |
L(r)(E,1)/r! |
Ω |
1.2374889908177 |
Real period |
R |
0.35480517563819 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17391j1 |
Quadratic twists by: -3 |