Atkin-Lehner |
2- 3- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368fe |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
67584 |
Modular degree for the optimal curve |
Δ |
-13663862784 = -1 · 217 · 36 · 11 · 13 |
Discriminant |
Eigenvalues |
2- 3- 3 -1 11- 13- -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-5196,144272] |
[a1,a2,a3,a4,a6] |
Generators |
[28:144:1] |
Generators of the group modulo torsion |
j |
-162365474/143 |
j-invariant |
L |
8.5937073666954 |
L(r)(E,1)/r! |
Ω |
1.247788577911 |
Real period |
R |
1.7217875523578 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001175 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
82368bj1 20592e1 9152x1 |
Quadratic twists by: -4 8 -3 |