Corollary ABGT-3a. Mumford-Ramanujam theorem for elliptic curves. If m : C × C ⟶ C is a binary morphism of a nonsingular cubic curve C defined over the complex projective plane, and if for some e in C, m(x, e) = m(e, x) = x for all x, then the structure ⟨C; m, e⟩ is an Abelian group.