ON ELLIPTIC CURVES WHOSE 3-TORSION SUBGROUP SPLITS AS μ₃ ⊕ Z/3Z
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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 $E[3]{\simeq}{\mu}_3{\oplus}\mathbb{Z}/3{\mathbb{Z}}$.
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 $E[3]{\simeq}{\mu}_3{\oplus}\mathbb{Z}/3{\mathbb{Z}}$.
참고문헌 (5)
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- J. H. Silverman, "The Arithmetic of Elliptic Curves, In Graduate Texts in Math" (1994), Springer-Verlag
- J. V´elu, "Isog´enis entre courbs elliptiques", C. R. Acad. Sci. Paris S´er. A-B, pp.238~241 (1971)