Let be m ∈ Z>0 and a, q ∈ Q. Denote by APm(a, q) the set of rational numbers d such that a, a + q, . . . , a + (m − 1)q form an arithmetic progression in the Edwards curve Ed : x2 +y2 = 1+d x2y2. We study the set APm(a, q) and we parametrize it by the rational points of an algebraic curve.