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Torsion Points on Certain Families of Elliptic Curves
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 2003
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