# ON ELLIPTIC CURVES WHOSE 3-TORSION SUBGROUP SPLITS AS μ3 ⊕ℤ/3ℤ

• Published : 2012.07.31

#### Abstract

In this paper, we study elliptic curves E over $\mathbb{Q}$ such that the 3-torsion subgroup E[3] is split as ${\mu}_3{\oplus}\mathbb{Z}/3{\mathbb{Z}}$. For a non-zero intege $m$, let $C_m$ denote the curve $x^3+y^3=m$. We consider the relation between the set of integral points of $C_m$ and the elliptic curves E with $E[3]{\simeq}{\mu}_3{\oplus}\mathbb{Z}/3{\mathbb{Z}}$.

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