Atkin-Lehner |
2+ 7+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
12992d |
Isogeny class |
Conductor |
12992 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
768 |
Modular degree for the optimal curve |
Δ |
-12992 = -1 · 26 · 7 · 29 |
Discriminant |
Eigenvalues |
2+ -1 2 7+ 0 0 6 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-7,-7] |
[a1,a2,a3,a4,a6] |
Generators |
[16:61:1] |
Generators of the group modulo torsion |
j |
-681472/203 |
j-invariant |
L |
4.0721802209151 |
L(r)(E,1)/r! |
Ω |
1.4286740051981 |
Real period |
R |
2.850321491186 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
12992n1 6496j1 116928bn1 90944s1 |
Quadratic twists by: -4 8 -3 -7 |