  In this article, we develop a geometric method to construct solutions of the
classical Yang-Baxter equation, attaching to the Weierstrass family of plane
cubic curves and a pair of coprime positive integers, a family of classical
r-matrices. It turns out that all elliptic r-matrices arise in this way from
smooth cubic curves. For the cuspidal cubic curve, we prove that the obtained
solutions are rational and compute them explicitly. We also describe them in
terms of Stolin's classification and prove that they are degenerations of the
corresponding elliptic solutions.
