Atkin-Lehner |
2- 3+ 17+ 83- |
Signs for the Atkin-Lehner involutions |
Class |
67728q |
Isogeny class |
Conductor |
67728 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1182720 |
Modular degree for the optimal curve |
Δ |
100138725874335744 = 234 · 35 · 172 · 83 |
Discriminant |
Eigenvalues |
2- 3+ -2 0 0 -4 17+ -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1932024,1034166384] |
[a1,a2,a3,a4,a6] |
Generators |
[794:274:1] |
Generators of the group modulo torsion |
j |
194715955430565041017/24447931121664 |
j-invariant |
L |
2.9408669202093 |
L(r)(E,1)/r! |
Ω |
0.32385828079656 |
Real period |
R |
4.5403608531779 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999895 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8466f1 |
Quadratic twists by: -4 |