if $e$ is an elliptic curve defined over a number field $k$, then it has been known for some time now that the group of $k$-rational points on $e$ is a finitely generated abelian group. the bsd, in its weak form, offers a conjectural link between the rank of $e(k)$ and the order of vanishing of a certain complex analytic l-function associated to $e$. the strong form of the bsd goes further and links the leading term of this l-function to certain algebraic invariants associated to $e$. in this talk i will sketch enough of the definitions, etc. to make this link more precise. despite all the fancy words, this talk should be accessible to everyone.