Atkin-Lehner |
2- 3- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368do |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
614400 |
Modular degree for the optimal curve |
Δ |
-136355526266978304 = -1 · 217 · 316 · 11 · 133 |
Discriminant |
Eigenvalues |
2- 3- -1 -3 11+ 13+ 0 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-174828,-33275824] |
[a1,a2,a3,a4,a6] |
Generators |
[538:5328:1] |
Generators of the group modulo torsion |
j |
-6184708364018/1427037183 |
j-invariant |
L |
3.3820038914079 |
L(r)(E,1)/r! |
Ω |
0.11532643781492 |
Real period |
R |
3.6656858076881 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001812 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
82368bq1 20592m1 27456bq1 |
Quadratic twists by: -4 8 -3 |