
In this paper we give a new formula for adding 2coverings and 3coverings of elliptic curves, that avoids the need for any field extensions. We show that the 6coverings obtained can be represented by pairs of cubic forms. We then prove a theorem on the existence of such models with integer coefficients and the same discriminant as a minimal model for the Jacobian elliptic curve. This work has applications to finding rational points of large height on elliptic curves.