Atkin-Lehner |
2- 3- 7- 13+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
82992cn |
Isogeny class |
Conductor |
82992 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
230400 |
Modular degree for the optimal curve |
Δ |
17818045120512 = 222 · 33 · 72 · 132 · 19 |
Discriminant |
Eigenvalues |
2- 3- -2 7- -2 13+ 0 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-27704,-1772460] |
[a1,a2,a3,a4,a6] |
Generators |
[-92:78:1] |
Generators of the group modulo torsion |
j |
574125551923897/4350108672 |
j-invariant |
L |
6.1646590203257 |
L(r)(E,1)/r! |
Ω |
0.37022097450802 |
Real period |
R |
1.3876079966342 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000005413 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
10374a1 |
Quadratic twists by: -4 |