Atkin-Lehner |
2- 3+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
12384j |
Isogeny class |
Conductor |
12384 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
2048 |
Modular degree for the optimal curve |
Δ |
-4755456 = -1 · 212 · 33 · 43 |
Discriminant |
Eigenvalues |
2- 3+ -3 -3 -1 -5 2 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,36,-64] |
[a1,a2,a3,a4,a6] |
Generators |
[2:4:1] [4:12:1] |
Generators of the group modulo torsion |
j |
46656/43 |
j-invariant |
L |
5.2741919004152 |
L(r)(E,1)/r! |
Ω |
1.3356904302298 |
Real period |
R |
0.49358292358091 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
12384k1 24768bu1 12384a1 |
Quadratic twists by: -4 8 -3 |