Atkin-Lehner |
5+ 29- 71+ |
Signs for the Atkin-Lehner involutions |
Class |
51475c |
Isogeny class |
Conductor |
51475 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
288768 |
Modular degree for the optimal curve |
Δ |
-364447021484375 = -1 · 514 · 292 · 71 |
Discriminant |
Eigenvalues |
-1 0 5+ 4 6 2 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-151005,-22566628] |
[a1,a2,a3,a4,a6] |
j |
-24371091085312089/23324609375 |
j-invariant |
L |
2.1795635356267 |
L(r)(E,1)/r! |
Ω |
0.1210868630144 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
10295a1 |
Quadratic twists by: 5 |