Curvas elípticas y el Teorema de Mordell

Abstract

Eliptic curves are mathematical objects that have interesting analytic, arithmetic and algebraic properties, though we’ll focus on the algebraic and arithmetic aspects only. We can define a natural geometric group law on them. Mordell’s theorem states that the subgroup of points with rational coordinates of and elliptic curve defined over Q is abelian and finitely generated and it’s usually a good first objective in the study of these curves. The proof is not elementary and eventually, we’ll need to use some tools of algebraic number theory.