Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve

Abstract

Let A be an abelian variety defined over a number field K, $E/K$ be an elliptic curve, and $\varphi :A\to E^m$ be an isogeny defined over K. Let $P\in A\left(K\right)$ be such that $\varphi \left(P\right)=(Q_1,\dots ,Q_m)$ with ${\mathrm{Rank}}_Z(〈Q_1,\dots ,Q_m〉)=1$. We will study a divisibility sequence related to the point P and show its relation with elliptic divisibility sequences.