Atkin-Lehner |
2- 3+ 83- |
Signs for the Atkin-Lehner involutions |
Class |
82668a |
Isogeny class |
Conductor |
82668 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1859760 |
Modular degree for the optimal curve |
Δ |
-316514898743009328 = -1 · 24 · 36 · 837 |
Discriminant |
Eigenvalues |
2- 3+ -4 4 4 2 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,128595,20393226] |
[a1,a2,a3,a4,a6] |
Generators |
[23161024598:693032986660:68417929] |
Generators of the group modulo torsion |
j |
44957696/60507 |
j-invariant |
L |
5.3496443144881 |
L(r)(E,1)/r! |
Ω |
0.20608728767176 |
Real period |
R |
12.979074007192 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999948063 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
996a1 |
Quadratic twists by: -83 |