Atkin-Lehner |
2+ 7+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
75712f |
Isogeny class |
Conductor |
75712 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
387072 |
Modular degree for the optimal curve |
Δ |
-58953743709765632 = -1 · 227 · 7 · 137 |
Discriminant |
Eigenvalues |
2+ -1 0 7+ -3 13+ 0 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,75487,-8554079] |
[a1,a2,a3,a4,a6] |
Generators |
[153:2560:1] |
Generators of the group modulo torsion |
j |
37595375/46592 |
j-invariant |
L |
3.4031020062124 |
L(r)(E,1)/r! |
Ω |
0.188311358923 |
Real period |
R |
2.2589595940363 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999969773 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
75712cn1 2366a1 5824i1 |
Quadratic twists by: -4 8 13 |