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Torsion points with multiplicatively dependent coordinates on elliptic curves
Author(s) -
Barroero Fabrizio,
Sha Min
Publication year - 2020
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12363
Subject(s) - mathematics , elliptic curve , torsion (gastropod) , multiplicative function , hessian form of an elliptic curve , schoof's algorithm , tripling oriented doche–icart–kohel curve , elliptic curve point multiplication , edwards curve , pure mathematics , modular elliptic curve , supersingular elliptic curve , complex multiplication , mathematical analysis , quarter period , medicine , surgery
In this paper, we study the finiteness problem of torsion points on an elliptic curve whose coordinates satisfy some multiplicative dependence relations. In particular, we prove that on an elliptic curve defined over a number field there are only finitely many torsion points whose coordinates are multiplicatively dependent. Moreover, we produce an effective result when the elliptic curve is defined over the rational numbers or has complex multiplication.