Atkin-Lehner |
3- 11- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
561c |
Isogeny class |
Conductor |
561 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
64 |
Modular degree for the optimal curve |
Δ |
-15147 = -1 · 34 · 11 · 17 |
Discriminant |
Eigenvalues |
-2 3- 0 -3 11- -4 17+ -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-8,8] |
[a1,a2,a3,a4,a6] |
Generators |
[1:1:1] |
Generators of the group modulo torsion |
j |
-64000000/15147 |
j-invariant |
L |
1.255819114575 |
L(r)(E,1)/r! |
Ω |
3.7556570476757 |
Real period |
R |
0.083595167146068 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8976n1 35904d1 1683i1 14025i1 |
Quadratic twists by: -4 8 -3 5 |