Atkin-Lehner |
2- 5+ 11+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
53680o |
Isogeny class |
Conductor |
53680 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
52992 |
Modular degree for the optimal curve |
Δ |
-687104000000 = -1 · 216 · 56 · 11 · 61 |
Discriminant |
Eigenvalues |
2- 0 5+ 4 11+ -4 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2443,61242] |
[a1,a2,a3,a4,a6] |
Generators |
[197:2688:1] |
Generators of the group modulo torsion |
j |
-393671672289/167750000 |
j-invariant |
L |
5.5483800628413 |
L(r)(E,1)/r! |
Ω |
0.84867499927963 |
Real period |
R |
3.2688485388835 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000139 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6710f1 |
Quadratic twists by: -4 |