Resumen de Elliptic curves with j-invariant equals 0 or 1728 over a finite prime field
Let p be a prime number, p ? 2,3 and Fp the finite field with p elements. An elliptic curve E over Fp is a projective nonsingular curve of genus 1 defined over Fp. Each one of these curves has an isomorphic model given by an (Weierstrass) equation E: y2 = x3 + Ax + B, A,B Î Fp with D = 4A3 + 27B2 ? 0. The j-invariant of E is defined by j(E) = 1728·4A3/D.
The aim of this note is to establish some results concerning the cardinality of the group of points on elliptic curves over Fp with j-invariants equals to 0 or 1728, and the connection between these cardinalities and some expressions of sum of squares.
