Abstract: This is a report on joint work with Mike Artin and Fernando Villegas. Let C -> S be a flat family of plane cubic curves over an arbitrary base scheme S, and J -> S be the degree 0 part of the relative Picard scheme of C/S. (Thus J is a group scheme over S, whose fiber at a point, s in S where the fiber of C is smooth, is the Jacobian of that fiber.) If 6 is invertible on S, then J is described in Weierstrass form by the classical invariants of ternary cubic forms. We give explicitly some less invariant functions which describe J in generalized Weierstrass form over an arbitrary base S.