Abstract
AbstractIn 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.
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