Resultants and discriminants of multiplication polynomials for elliptic curves

Abstract

In this article, we prove that the resultant of the standard multiplication polynomials An, Bn of an elliptic curve in the form y2=x3+ax+b is (16Δ)n2(n2−1)6, where Δ=−(4a3+27b2) is the discriminant of the curve. We give an application to good reduction of an associated Lattès map. We also prove a similar result for the discriminant of the largest squarefree factor of Bn.