The number of rational points on singular curves y2 = x(x - a)2 over finite fields Fp

Abstract

Let p ≥ 5 be a prime number and let F<inf>p</inf> be a finite field. In this work, we determine the number of rational points on singular curves E<inf>a</inf>: y² = x(x - a)² over F<inf>p</inf> for some specific values of a.