Atkin-Lehner |
2- 3- 7- 13+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
82992cm |
Isogeny class |
Conductor |
82992 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
211968 |
Modular degree for the optimal curve |
Δ |
-74020321550448 = -1 · 24 · 32 · 78 · 13 · 193 |
Discriminant |
Eigenvalues |
2- 3- 0 7- -4 13+ 7 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,9422,-214669] |
[a1,a2,a3,a4,a6] |
Generators |
[35:399:1] |
Generators of the group modulo torsion |
j |
5780786562464000/4626270096903 |
j-invariant |
L |
8.4082026376249 |
L(r)(E,1)/r! |
Ω |
0.34064330918209 |
Real period |
R |
0.51423551700712 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004086 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
20748a1 |
Quadratic twists by: -4 |