Atkin-Lehner |
2+ 3- 5+ 11- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
82170o |
Isogeny class |
Conductor |
82170 |
Conductor |
∏ cp |
28 |
Product of Tamagawa factors cp |
deg |
1599360 |
Modular degree for the optimal curve |
Δ |
-4584380674149936000 = -1 · 27 · 311 · 53 · 117 · 83 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -1 11- 1 0 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-684765,241377925] |
[a1,a2,a3,a4,a6] |
Generators |
[503:4649:1] |
Generators of the group modulo torsion |
j |
-48710344796154847441/6288588030384000 |
j-invariant |
L |
3.4318438192228 |
L(r)(E,1)/r! |
Ω |
0.23717676351297 |
Real period |
R |
0.51677006112831 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000008788 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27390r1 |
Quadratic twists by: -3 |