Atkin-Lehner |
2+ 31+ 53- |
Signs for the Atkin-Lehner involutions |
Class |
3286c |
Isogeny class |
Conductor |
3286 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1280 |
Modular degree for the optimal curve |
Δ |
-13038848 = -1 · 28 · 312 · 53 |
Discriminant |
Eigenvalues |
2+ -3 -2 -2 0 -5 -1 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-28,-176] |
[a1,a2,a3,a4,a6] |
Generators |
[8:4:1] [9:11:1] |
Generators of the group modulo torsion |
j |
-2476813977/13038848 |
j-invariant |
L |
1.9473788004205 |
L(r)(E,1)/r! |
Ω |
0.93290010925182 |
Real period |
R |
0.52186155331856 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999983 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
26288j1 105152c1 29574i1 82150h1 |
Quadratic twists by: -4 8 -3 5 |