Atkin-Lehner |
2+ 3- 13- |
Signs for the Atkin-Lehner involutions |
Class |
12168j |
Isogeny class |
Conductor |
12168 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
4608 |
Modular degree for the optimal curve |
Δ |
-1230038784 = -1 · 28 · 37 · 133 |
Discriminant |
Eigenvalues |
2+ 3- 2 2 -4 13- 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-39,1690] |
[a1,a2,a3,a4,a6] |
Generators |
[3:40:1] |
Generators of the group modulo torsion |
j |
-16/3 |
j-invariant |
L |
5.6283414750092 |
L(r)(E,1)/r! |
Ω |
1.2534799686498 |
Real period |
R |
2.2450863259794 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
24336u1 97344df1 4056r1 12168w1 |
Quadratic twists by: -4 8 -3 13 |