Atkin-Lehner |
2+ 3- 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368bc |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
26378087104512 = 216 · 39 · 112 · 132 |
Discriminant |
Eigenvalues |
2+ 3- 0 4 11+ 13- -8 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-19020,978928] |
[a1,a2,a3,a4,a6] |
Generators |
[-88:1404:1] |
Generators of the group modulo torsion |
j |
15927506500/552123 |
j-invariant |
L |
7.2589498467211 |
L(r)(E,1)/r! |
Ω |
0.66417926277513 |
Real period |
R |
1.3661503475848 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001557 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368ew2 10296e2 27456bg2 |
Quadratic twists by: -4 8 -3 |