Albime triangles over quadratic fields

Abstract

This note uses a diophantine problem arising in elementary geometry as a prerequisite to illustrate some theory of elliptic curves. As a typical example, Proposition~\ref {5.3} and Theorem~\ref {main} determine the exact set of ration\-al numbers for which the specialization homomorphism from the torsion free rank~2 group of rational points on some elliptic curve over $\mathbb {Q}(t)$, is well defined and injective.