Atkin-Lehner |
2+ 3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368bn |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
691200 |
Modular degree for the optimal curve |
Δ |
-274738523821572096 = -1 · 223 · 36 · 112 · 135 |
Discriminant |
Eigenvalues |
2+ 3- 1 3 11- 13+ -3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,161268,-3822608] |
[a1,a2,a3,a4,a6] |
Generators |
[6474:188288:27] |
Generators of the group modulo torsion |
j |
2427173723519/1437646496 |
j-invariant |
L |
8.0316642395894 |
L(r)(E,1)/r! |
Ω |
0.18103113705346 |
Real period |
R |
5.5457754185334 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000881 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
82368dl1 2574h1 9152a1 |
Quadratic twists by: -4 8 -3 |