Atkin-Lehner |
2- 3+ 7+ 13+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
82992bo |
Isogeny class |
Conductor |
82992 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
2532096 |
Modular degree for the optimal curve |
Δ |
10875831915089232 = 24 · 32 · 77 · 136 · 19 |
Discriminant |
Eigenvalues |
2- 3+ -2 7+ 4 13+ 4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-5217969,4589493480] |
[a1,a2,a3,a4,a6] |
Generators |
[1212455706:-1824703287:941192] |
Generators of the group modulo torsion |
j |
981992784253918614863872/679739494693077 |
j-invariant |
L |
4.6591332521574 |
L(r)(E,1)/r! |
Ω |
0.33530835197087 |
Real period |
R |
13.89507068684 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999992151 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
20748m1 |
Quadratic twists by: -4 |