Atkin-Lehner |
2- 3- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368dj |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
11723594268672 = 218 · 37 · 112 · 132 |
Discriminant |
Eigenvalues |
2- 3- 0 0 11+ 13+ 4 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-7500,188048] |
[a1,a2,a3,a4,a6] |
Generators |
[2:416:1] |
Generators of the group modulo torsion |
j |
244140625/61347 |
j-invariant |
L |
6.0549025423148 |
L(r)(E,1)/r! |
Ω |
0.67040266001783 |
Real period |
R |
1.1289675039392 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000989 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368bm2 20592bq2 27456bp2 |
Quadratic twists by: -4 8 -3 |