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In this paper, we study the finiteness problem of torsion points on anelliptic curve whose coordinates satisfy some multiplicative dependencerelations. In particular, we prove that on an elliptic curve defined over anumber field there are only finitely many torsion points whose coordinates aremultiplicatively dependent. Moreover, we produce an effective result when theelliptic curve is defined over the rational numbers or has complexmultiplication.

Torsion points with multiplicatively dependent coordinates on elliptic curves