Atkin-Lehner |
2+ 3- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368cl |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
96 |
Product of Tamagawa factors cp |
deg |
405504 |
Modular degree for the optimal curve |
Δ |
-206304259239936 = -1 · 212 · 37 · 116 · 13 |
Discriminant |
Eigenvalues |
2+ 3- -2 -4 11- 13- -4 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-31476,2257760] |
[a1,a2,a3,a4,a6] |
Generators |
[157:1089:1] [-140:1980:1] |
Generators of the group modulo torsion |
j |
-1154981015488/69090879 |
j-invariant |
L |
8.703634967566 |
L(r)(E,1)/r! |
Ω |
0.55524718297939 |
Real period |
R |
0.65313515872389 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998809 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368bi1 41184i1 27456i1 |
Quadratic twists by: -4 8 -3 |