Atkin-Lehner |
2+ 5- 7+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
69440bq |
Isogeny class |
Conductor |
69440 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
-19054336000000 = -1 · 214 · 56 · 74 · 31 |
Discriminant |
Eigenvalues |
2+ 2 5- 7+ 4 -4 0 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-32625,-2267023] |
[a1,a2,a3,a4,a6] |
Generators |
[3737:228144:1] |
Generators of the group modulo torsion |
j |
-234405957659344/1162984375 |
j-invariant |
L |
10.486056366784 |
L(r)(E,1)/r! |
Ω |
0.17756278205115 |
Real period |
R |
4.9212904892224 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000196 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69440dp1 8680e1 |
Quadratic twists by: -4 8 |