Atkin-Lehner |
3- 7+ 11- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
82467i |
Isogeny class |
Conductor |
82467 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
159264 |
Modular degree for the optimal curve |
Δ |
-227117865382947 = -1 · 36 · 78 · 11 · 173 |
Discriminant |
Eigenvalues |
0 3- 0 7+ 11- -4 17+ 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-10290,828945] |
[a1,a2,a3,a4,a6] |
Generators |
[-49:1102:1] |
Generators of the group modulo torsion |
j |
-28672000/54043 |
j-invariant |
L |
4.2352293196881 |
L(r)(E,1)/r! |
Ω |
0.49846217394642 |
Real period |
R |
1.4160985323591 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004523 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9163a1 82467ba1 |
Quadratic twists by: -3 -7 |