2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150240In this paper we give a detailed proof of a result we announced a year ago. This result is an effective version of the theorem of Mazur-Kamienny-Merel concerning uniform bounds for rational torsion points on elliptic curves over number fields.LaTeX, 33 pages with 2 figures, hard copy available in a few days; send email to edix@univ-rennes1.frAlgebraic Geometry14G05 11G05text