Atkin-Lehner |
2- 3- 13- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
72384do |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
55296 |
Modular degree for the optimal curve |
Δ |
-80627017536 = -1 · 26 · 32 · 136 · 29 |
Discriminant |
Eigenvalues |
2- 3- -2 -2 0 13- -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-384,-14094] |
[a1,a2,a3,a4,a6] |
Generators |
[81:702:1] [861:25272:1] |
Generators of the group modulo torsion |
j |
-98099748928/1259797149 |
j-invariant |
L |
10.721556003066 |
L(r)(E,1)/r! |
Ω |
0.4624495095125 |
Real period |
R |
7.7280912348498 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999944 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
72384cg1 36192d2 |
Quadratic twists by: -4 8 |