This Chapter contains descriptions for functions pertaining to arithmetic with elliptic curves. The category to which elliptic curves belong is called GeomEC, points on curves are of type GeomECElt, and there also exists a special category for Kodaira symbols KodSym.

This module is currently under construction; the main functions that are present deal with elementary arithmetic over fields, and with more sophisticated questions over the rational field. The latter include functions for minimal models and local information (Tate's algorithm). The computation of the Mordell-Weil group of a curve is to follow soon. These facilities are based on implementations by John Cremona. We refer to his book for details.

For the time being, there is a restriction on elliptic curves to be defined over fields.