Atkin-Lehner |
2- 3- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368dn |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
76800 |
Modular degree for the optimal curve |
Δ |
-22203777024 = -1 · 214 · 36 · 11 · 132 |
Discriminant |
Eigenvalues |
2- 3- -1 2 11+ 13+ 0 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-8688,311776] |
[a1,a2,a3,a4,a6] |
Generators |
[33:247:1] |
Generators of the group modulo torsion |
j |
-6072054784/1859 |
j-invariant |
L |
5.9241079566606 |
L(r)(E,1)/r! |
Ω |
1.1804716101685 |
Real period |
R |
2.5092123801978 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999987291 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
82368bp1 20592l1 9152y1 |
Quadratic twists by: -4 8 -3 |