Atkin-Lehner |
2+ 5- 7- 13- |
Signs for the Atkin-Lehner involutions |
Class |
82810bo |
Isogeny class |
Conductor |
82810 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
165888 |
Modular degree for the optimal curve |
Δ |
2067798824000 = 26 · 53 · 76 · 133 |
Discriminant |
Eigenvalues |
2+ -2 5- 7- 0 13- -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-3358,28368] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:197:1] [-51:285:1] |
Generators of the group modulo torsion |
j |
16194277/8000 |
j-invariant |
L |
6.312059175134 |
L(r)(E,1)/r! |
Ω |
0.73326336957068 |
Real period |
R |
0.71734789038406 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000071 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
1690d1 82810cf1 |
Quadratic twists by: -7 13 |