Atkin-Lehner |
2- 3- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
6768p |
Isogeny class |
Conductor |
6768 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
3072 |
Modular degree for the optimal curve |
Δ |
-11367641088 = -1 · 212 · 310 · 47 |
Discriminant |
Eigenvalues |
2- 3- -2 0 4 -2 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-291,5474] |
[a1,a2,a3,a4,a6] |
Generators |
[1:72:1] |
Generators of the group modulo torsion |
j |
-912673/3807 |
j-invariant |
L |
3.6685494569659 |
L(r)(E,1)/r! |
Ω |
1.1113738291217 |
Real period |
R |
0.82522850566515 |
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 |
423c1 27072ce1 2256j1 |
Quadratic twists by: -4 8 -3 |