Atkin-Lehner |
2+ 3- 5- 11+ 83+ |
Signs for the Atkin-Lehner involutions |
Class |
82170u |
Isogeny class |
Conductor |
82170 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
40704 |
Modular degree for the optimal curve |
Δ |
-585707760 = -1 · 24 · 36 · 5 · 112 · 83 |
Discriminant |
Eigenvalues |
2+ 3- 5- 0 11+ 6 0 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-54,1188] |
[a1,a2,a3,a4,a6] |
Generators |
[4:30:1] |
Generators of the group modulo torsion |
j |
-24137569/803440 |
j-invariant |
L |
5.7602330382166 |
L(r)(E,1)/r! |
Ω |
1.3616134511935 |
Real period |
R |
2.115223314159 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000007886 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
9130f1 |
Quadratic twists by: -3 |