2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73171We work out the complete descent via 4-isogeny for a family of rational elliptic curves with a rational point of order 4; such a family is of the form $y^2 + x y + a y = x^3 + a x^2$ where $\sqrt{-a} \in \mathbb Q^\times$. In the process we exhibit the 4-isogeny and the isogenous curve, explicitly present the principal homogeneous spaces, and discuss examples by computing the rank.20 pagesNumber Theory14G05; 11G05; 11D25text