Atkin-Lehner |
2- 3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368eq |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
Δ |
316537045254144 = 218 · 310 · 112 · 132 |
Discriminant |
Eigenvalues |
2- 3- -2 0 11- 13+ 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-247116,47274640] |
[a1,a2,a3,a4,a6] |
Generators |
[-288:9724:1] [128:4212:1] |
Generators of the group modulo torsion |
j |
8732907467857/1656369 |
j-invariant |
L |
10.144591023334 |
L(r)(E,1)/r! |
Ω |
0.52748457433213 |
Real period |
R |
4.8080036446455 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998046 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
82368w2 20592bg2 27456bz2 |
Quadratic twists by: -4 8 -3 |