Atkin-Lehner |
2+ 3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368bq |
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 |
[182:2736:1] |
Generators of the group modulo torsion |
j |
-6184708364018/1427037183 |
j-invariant |
L |
7.2214502786921 |
L(r)(E,1)/r! |
Ω |
0.31295278312241 |
Real period |
R |
2.884400884895 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002968 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
82368do1 10296m1 27456v1 |
Quadratic twists by: -4 8 -3 |