2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78430We consider the practical computation of rational points on y^2=x(x^2+ax+b). The algebra necessary for a 4-descent procedure is described. A simple further descent is then described which only uses integer arithmetic. Numerous examples are given to illustrate the effectiveness of this extra descent. Currently, the largest point found has height 51.15 or 102.3, depending on which height normalisation you use.14 pages, Latex2eNumber Theory11G05, 11Y50 (Primary) 11D25(Secondary)text