Atkin-Lehner |
2+ 3+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368l |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
20480 |
Modular degree for the optimal curve |
Δ |
35335872 = 26 · 33 · 112 · 132 |
Discriminant |
Eigenvalues |
2+ 3+ -2 -2 11- 13- 4 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-471,3924] |
[a1,a2,a3,a4,a6] |
Generators |
[16:22:1] |
Generators of the group modulo torsion |
j |
6687175104/20449 |
j-invariant |
L |
4.9245197332935 |
L(r)(E,1)/r! |
Ω |
2.0710649330969 |
Real period |
R |
1.1888858859084 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999954841 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368g1 41184b2 82368e1 |
Quadratic twists by: -4 8 -3 |