Atkin-Lehner |
2+ 3+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
83232a |
Isogeny class |
Conductor |
83232 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
13312 |
Modular degree for the optimal curve |
Δ |
-8489664 = -1 · 26 · 33 · 173 |
Discriminant |
Eigenvalues |
2+ 3+ 2 0 0 6 17+ 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,51,0] |
[a1,a2,a3,a4,a6] |
Generators |
[25:130:1] |
Generators of the group modulo torsion |
j |
1728 |
j-invariant |
L |
8.3644595682035 |
L(r)(E,1)/r! |
Ω |
1.3876012233322 |
Real period |
R |
3.0139997806236 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003312 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
83232a1 83232ba1 83232b1 |
Quadratic twists by: -4 -3 17 |