Atkin-Lehner |
2+ 3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368br |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
67543889707008 = 215 · 38 · 11 · 134 |
Discriminant |
Eigenvalues |
2+ 3- 2 0 11- 13+ 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-40044,3058832] |
[a1,a2,a3,a4,a6] |
Generators |
[-214:1352:1] |
Generators of the group modulo torsion |
j |
297275150024/2827539 |
j-invariant |
L |
8.396411418936 |
L(r)(E,1)/r! |
Ω |
0.62106629241655 |
Real period |
R |
1.6899185157738 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002756 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368t3 41184l3 27456c3 |
Quadratic twists by: -4 8 -3 |