2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/86979A formalism is given to count integer and rational solutions to polynomial equations with rational coefficients. These polynomials $P(x)$ are parameterized by three integers, labeling an elliptic curve. The counting of the rational solutions to $y^2=P(x)$ is facilitated by another elliptic curve with integral coefficients. The problem of counting is described by two elliptic curves and a map between them.7 pages, LaTeXGeneral Physicstext