Atkin-Lehner |
2- 7+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
12992ba |
Isogeny class |
Conductor |
12992 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
3072 |
Modular degree for the optimal curve |
Δ |
-1140801536 = -1 · 214 · 74 · 29 |
Discriminant |
Eigenvalues |
2- -1 1 7+ 1 -1 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-145,-1711] |
[a1,a2,a3,a4,a6] |
Generators |
[55:392:1] |
Generators of the group modulo torsion |
j |
-20720464/69629 |
j-invariant |
L |
3.8170559697248 |
L(r)(E,1)/r! |
Ω |
0.63236340846665 |
Real period |
R |
1.5090436601085 |
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 |
12992q1 3248f1 116928di1 90944dq1 |
Quadratic twists by: -4 8 -3 -7 |