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

General Mathematics
Applied Mathematics

Access to Document

10.4134/CKMS.2012.27.3.497

Cite this

@article{aa79273e1619404a806cee9c639c8a81,

title = "On elliptic curves whose 3-torsion subgroup splits as μ3 ⊕ ℤ/3ℤ",

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.",

author = "Masaya Yasuda",

year = "2012",

doi = "10.4134/CKMS.2012.27.3.497",

language = "English",

volume = "27",

pages = "497--503",

journal = "Communications of the Korean Mathematical Society",

issn = "1225-1763",

publisher = "Korean Mathematical Society",

number = "3",

}

TY - JOUR

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

AU - Yasuda, Masaya

PY - 2012

Y1 - 2012

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 - https://www.scopus.com/pages/publications/84871409971

UR - https://www.scopus.com/pages/publications/84871409971#tab=citedBy

U2 - 10.4134/CKMS.2012.27.3.497

DO - 10.4134/CKMS.2012.27.3.497

M3 - Article

AN - SCOPUS:84871409971

SN - 1225-1763

VL - 27

SP - 497

EP - 503

JO - Communications of the Korean Mathematical Society

JF - Communications of the Korean Mathematical Society

IS - 3

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this