Tom Fisher's Home Page
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In this paper we give a new formula for adding 2-coverings and 3-coverings of elliptic curves, that avoids the need for any field extensions. We show that the 6-coverings 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.
