Atkin-Lehner |
2+ 3- 5- 11- 83- |
Signs for the Atkin-Lehner involutions |
Class |
82170bc |
Isogeny class |
Conductor |
82170 |
Conductor |
∏ cp |
140 |
Product of Tamagawa factors cp |
deg |
1128960 |
Modular degree for the optimal curve |
Δ |
198974855648868750 = 2 · 39 · 55 · 117 · 83 |
Discriminant |
Eigenvalues |
2+ 3- 5- -2 11- 7 0 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-155349,-9699345] |
[a1,a2,a3,a4,a6] |
Generators |
[-219:3822:1] |
Generators of the group modulo torsion |
j |
568752269081079889/272942188818750 |
j-invariant |
L |
5.6655888207329 |
L(r)(E,1)/r! |
Ω |
0.2522106737583 |
Real period |
R |
0.16045511072294 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999983365 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27390y1 |
Quadratic twists by: -3 |