This section involves elliptic curves with coefficients in a function field k(C) where C is a regular projective curve over some field k (usually a number field or a finite field). The commands are largely parallel to those for elliptic curves over the rationals; one can compute local information (Tate's algorithm and so forth), a minimal model, the L-function, the 2-Selmer group, and the Mordell--Weil group. This goes in order of decreasing generality: Local information is available for curves over univariate function fields over any exact base field, while at the other extreme Mordell--Weil groups are available only for curves over rational function fields over finite fields for which the associated surface is a rational surface. The generality of many of the commands will be expanded in future releases.

V2.28, 13 July 2023