Atkin-Lehner |
2- 3+ 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
122304fb |
Isogeny class |
Conductor |
122304 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
184320 |
Modular degree for the optimal curve |
Δ |
-14806222651584 = -1 · 26 · 32 · 711 · 13 |
Discriminant |
Eigenvalues |
2- 3+ -1 7- 0 13+ 0 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,6109,-24471] |
[a1,a2,a3,a4,a6] |
Generators |
[586:7203:8] |
Generators of the group modulo torsion |
j |
3348071936/1966419 |
j-invariant |
L |
4.2814731021531 |
L(r)(E,1)/r! |
Ω |
0.41229087306884 |
Real period |
R |
1.2980741719924 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000076428 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
122304hd1 61152by1 17472cz1 |
Quadratic twists by: -4 8 -7 |