Atkin-Lehner |
5+ 13+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
75205a |
Isogeny class |
Conductor |
75205 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
268800 |
Modular degree for the optimal curve |
Δ |
45375021355625 = 54 · 138 · 89 |
Discriminant |
Eigenvalues |
1 0 5+ 4 4 13+ 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-54365,4881800] |
[a1,a2,a3,a4,a6] |
Generators |
[6007976:-64626216:68921] |
Generators of the group modulo torsion |
j |
3681512411121/9400625 |
j-invariant |
L |
7.8309944029948 |
L(r)(E,1)/r! |
Ω |
0.64082922599312 |
Real period |
R |
12.220095599793 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999977236 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
5785b1 |
Quadratic twists by: 13 |