Atkin-Lehner |
2+ 3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368bm |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
65536 |
Modular degree for the optimal curve |
Δ |
-245949530112 = -1 · 218 · 38 · 11 · 13 |
Discriminant |
Eigenvalues |
2+ 3- 0 0 11- 13+ 4 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,1140,-18704] |
[a1,a2,a3,a4,a6] |
Generators |
[782:21888:1] |
Generators of the group modulo torsion |
j |
857375/1287 |
j-invariant |
L |
7.3268163966467 |
L(r)(E,1)/r! |
Ω |
0.52248796027149 |
Real period |
R |
3.5057345597274 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999988886 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368dj1 1287c1 27456u1 |
Quadratic twists by: -4 8 -3 |