Atkin-Lehner |
2+ 3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368bw |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
344064 |
Modular degree for the optimal curve |
Δ |
-6637498574294016 = -1 · 210 · 320 · 11 · 132 |
Discriminant |
Eigenvalues |
2+ 3- -2 -2 11- 13+ 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3936,-3920920] |
[a1,a2,a3,a4,a6] |
Generators |
[842:24284:1] |
Generators of the group modulo torsion |
j |
-9033613312/8891539371 |
j-invariant |
L |
4.6870394300001 |
L(r)(E,1)/r! |
Ω |
0.19027436360726 |
Real period |
R |
6.1582644956367 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999971627 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368ds1 5148c1 27456a1 |
Quadratic twists by: -4 8 -3 |