### Abstract

In this paper, we study elliptic curves E over ( such thatthe 3-torsion subgroup E[3] is split as μ_{3} ⊕ ℤ/3ℤ. For a non-zero integer 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] ≃ μ_{3} ⊕ ℤ/3ℤ.

Original language | English |
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Pages (from-to) | 497-503 |

Number of pages | 7 |

Journal | Communications of the Korean Mathematical Society |

Volume | 27 |

Issue number | 3 |

DOIs | |

Publication status | Published - Dec 27 2012 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

**On elliptic curves whose 3-torsion subgroup splits as μ3 ⊕ ℤ/3ℤ.** / Yasuda, Masaya.

Research output: Contribution to journal › Article

*Communications of the Korean Mathematical Society*, vol. 27, no. 3, pp. 497-503. https://doi.org/10.4134/CKMS.2012.27.3.497

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TY - JOUR

T1 - On elliptic curves whose 3-torsion subgroup splits as μ3 ⊕ ℤ/3ℤ

AU - Yasuda, Masaya

PY - 2012/12/27

Y1 - 2012/12/27

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84871409971&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84871409971&partnerID=8YFLogxK

U2 - 10.4134/CKMS.2012.27.3.497

DO - 10.4134/CKMS.2012.27.3.497

M3 - Article

VL - 27

SP - 497

EP - 503

JO - Communications of the Korean Mathematical Society

JF - Communications of the Korean Mathematical Society

SN - 1225-1763

IS - 3

ER -