2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149780We prove that there exist infinitely many elliptic curves over \Q with given modular invariant, and rank >=2. Furthermore, there exist infinitely many elliptic curves over $\Q$ with invariant equal at 0 (resp. 1728) and rank >=6 (resp. >=4).4 pages. (A paraitre aux Comptes-Rendus de l'Acad. des Sc. de Paris.)Algebraic Geometrytext