Atkin-Lehner |
2+ 3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368bw |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
90272408593416192 = 214 · 313 · 112 · 134 |
Discriminant |
Eigenvalues |
2+ 3- -2 -2 11- 13+ 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-397596,-95407504] |
[a1,a2,a3,a4,a6] |
Generators |
[-350:936:1] |
Generators of the group modulo torsion |
j |
581972233018192/7558011747 |
j-invariant |
L |
4.6870394300001 |
L(r)(E,1)/r! |
Ω |
0.19027436360726 |
Real period |
R |
3.0791322478184 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999971627 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368ds2 5148c2 27456a2 |
Quadratic twists by: -4 8 -3 |