On elliptic curves whose 3-torsion subgroup splits as μ3 ⊕ ℤ/3ℤ

Masaya Yasuda

doi:10.4134/CKMS.2012.27.3.497

On elliptic curves whose 3-torsion subgroup splits as μ3 ⊕ ℤ/3ℤ

Masaya Yasuda

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we study elliptic curves E over ( such thatthe 3-torsion subgroup E[3] is split as μ₃ ⊕ ℤ/3ℤ. For a non-zero integer m, let C_m denote the curve x³ + y³ = m. We consider the relation between the set of integral points of C_m and the elliptic curves E with E[3] ≃ μ₃ ⊕ ℤ/3ℤ.

Original language	English
Pages (from-to)	497-503
Number of pages	7
Journal	Communications of the Korean Mathematical Society
Volume	27
Issue number	3
DOIs	https://doi.org/10.4134/CKMS.2012.27.3.497
Publication status	Published - 2012
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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10.4134/CKMS.2012.27.3.497

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abstract = "In this paper, we study elliptic curves E over ( such thatthe 3-torsion subgroup E[3] is split as μ3 ⊕ ℤ/3ℤ. For a non-zero integer m, let Cm denote the curve x3 + y3 = m. We consider the relation between the set of integral points of Cm and the elliptic curves E with E[3] ≃ μ3 ⊕ ℤ/3ℤ.",

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AB - In this paper, we study elliptic curves E over ( such thatthe 3-torsion subgroup E[3] is split as μ3 ⊕ ℤ/3ℤ. For a non-zero integer m, let Cm denote the curve x3 + y3 = m. We consider the relation between the set of integral points of Cm and the elliptic curves E with E[3] ≃ μ3 ⊕ ℤ/3ℤ.

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On elliptic curves whose 3-torsion subgroup splits as μ3 ⊕ ℤ/3ℤ

Abstract

All Science Journal Classification (ASJC) codes

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