Abstract. We give two parametrizations of points on Edwards curves that omit the X coordinate. The first parametrization leads to a differential addition formula that has the cost 5M + 4S, a doubling formula that has the cost 5S and a tripling formula that costs 4M+7S. The second one yields a differential addition formula with cost 5M + 2S and a doubling formula with cost 5S both even on generalized Edwards curves. The price to pay for this representation is the extraction of two square roots in the ground field. For both parametrizations the formula for recovering the missing coordinate is also provided. In addition, we give an addition chain for computing the scalar multiple of a point on the Edwards curve.