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Torsion Points on Certain Families of Elliptic Curves

Published online by Cambridge University Press:  20 November 2018

Małgorzata Wieczorek
Małgorzata Wieczorek*
Affiliation:
University of Szczecin, Institute of Mathematics, ul. Wielkopolska 15, 70-451 Szczecin, Poland, email: wieczorek@wmf.univ.szczecin.pl
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Abstract

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Fix an elliptic curve ${{y}^{2}}\,=\,{{x}^{3}}\,+\,Ax\,+\,B$, satisfying $A,\,B\,\in \,\mathbb{Z},\,A\ge \,\left| B \right|\,>\,0$. We prove that the $\mathbb{Q}$-torsion subgroup is one of $(0),\,\mathbb{Z}/3\mathbb{Z},\,\mathbb{Z}/9\mathbb{Z}$. Related numerical calculations are discussed.

Keywords

11G05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 1 , 01 March 2003 , pp. 157 - 160
Copyright
Copyright © Canadian Mathematical Society 2003

References

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