Atkin-Lehner |
2- 3+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
6768j |
Isogeny class |
Conductor |
6768 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
2304 |
Modular degree for the optimal curve |
Δ |
236825856 = 28 · 39 · 47 |
Discriminant |
Eigenvalues |
2- 3+ 3 -3 1 -4 4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-216,972] |
[a1,a2,a3,a4,a6] |
Generators |
[18:54:1] |
Generators of the group modulo torsion |
j |
221184/47 |
j-invariant |
L |
4.5131236892112 |
L(r)(E,1)/r! |
Ω |
1.6640453031576 |
Real period |
R |
0.67803497907291 |
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 |
1692a1 27072bu1 6768i1 |
Quadratic twists by: -4 8 -3 |