Atkin-Lehner |
2+ 3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368bo |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
55296 |
Modular degree for the optimal curve |
Δ |
-54655451136 = -1 · 219 · 36 · 11 · 13 |
Discriminant |
Eigenvalues |
2+ 3- 1 -3 11- 13+ 6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-12,11248] |
[a1,a2,a3,a4,a6] |
Generators |
[8:108:1] |
Generators of the group modulo torsion |
j |
-1/286 |
j-invariant |
L |
6.4191845137765 |
L(r)(E,1)/r! |
Ω |
0.8908597351864 |
Real period |
R |
1.801401573187 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999402 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
82368dk1 2574i1 9152d1 |
Quadratic twists by: -4 8 -3 |