Atkin-Lehner |
2- 3+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368ct |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
-278618545041408 = -1 · 212 · 39 · 112 · 134 |
Discriminant |
Eigenvalues |
2- 3+ 0 4 11+ 13- 4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,11340,654912] |
[a1,a2,a3,a4,a6] |
Generators |
[277:5005:1] |
Generators of the group modulo torsion |
j |
2000376000/3455881 |
j-invariant |
L |
8.2567373381711 |
L(r)(E,1)/r! |
Ω |
0.37633401237182 |
Real period |
R |
2.7424897389739 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999991744 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368de2 41184u1 82368dd2 |
Quadratic twists by: -4 8 -3 |