Atkin-Lehner |
3+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
867a |
Isogeny class |
Conductor |
867 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
576 |
Modular degree for the optimal curve |
Δ |
-11079144171 = -1 · 33 · 177 |
Discriminant |
Eigenvalues |
0 3+ -3 4 3 -1 17+ -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,193,-5023] |
[a1,a2,a3,a4,a6] |
Generators |
[57:433:1] |
Generators of the group modulo torsion |
j |
32768/459 |
j-invariant |
L |
1.6987250822621 |
L(r)(E,1)/r! |
Ω |
0.62578485313359 |
Real period |
R |
0.67863782326937 |
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 |
13872bn1 55488bp1 2601g1 21675p1 |
Quadratic twists by: -4 8 -3 5 |