Elliptic curves with the real ℘-function

Hwasin Park; Aeran Kim; Daeyeoul Kim; Minhee Kim

Elliptic curves with the real ℘-function

Hwasin Park^*
, Aeran Kim
, Daeyeoul Kim
, Minhee Kim

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

Abstract

Let E: Y₂ = 4x₃ + Ax + B, with A, B ∈ ℝ be an elliptic curve defined over ℝ. We know that E(C) ≃ C/L for some lattice L. The goal of this paper is to show that L is either rectangular or a special shape of parallelogram and deduce that for g₂ (τ), g₃(τ) ∈ ℝ, the Weierstrass ℘-function has real number.

Original language	English
Pages (from-to)	249-255
Number of pages	7
Journal	JP Journal of Algebra, Number Theory and Applications
Volume	23
Issue number	2
State	Published - 2011.12

Keywords

The Weierstrass ℘-function

Quacquarelli Symonds(QS) Subject Topics

Mathematics

Cite this

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title = "Elliptic curves with the real ℘-function",

abstract = "Let E: Y2 = 4x3 + Ax + B, with A, B ∈ ℝ be an elliptic curve defined over ℝ. We know that E(C) ≃ C/L for some lattice L. The goal of this paper is to show that L is either rectangular or a special shape of parallelogram and deduce that for g2 (τ), g3(τ) ∈ ℝ, the Weierstrass ℘-function has real number.",

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T1 - Elliptic curves with the real ℘-function

AU - Park, Hwasin

AU - Kim, Aeran

AU - Kim, Daeyeoul

AU - Kim, Minhee

PY - 2011/12

Y1 - 2011/12

N2 - Let E: Y2 = 4x3 + Ax + B, with A, B ∈ ℝ be an elliptic curve defined over ℝ. We know that E(C) ≃ C/L for some lattice L. The goal of this paper is to show that L is either rectangular or a special shape of parallelogram and deduce that for g2 (τ), g3(τ) ∈ ℝ, the Weierstrass ℘-function has real number.

AB - Let E: Y2 = 4x3 + Ax + B, with A, B ∈ ℝ be an elliptic curve defined over ℝ. We know that E(C) ≃ C/L for some lattice L. The goal of this paper is to show that L is either rectangular or a special shape of parallelogram and deduce that for g2 (τ), g3(τ) ∈ ℝ, the Weierstrass ℘-function has real number.

KW - The Weierstrass ℘-function

UR - https://www.scopus.com/pages/publications/80955150906

M3 - Journal article

AN - SCOPUS:80955150906

SN - 0972-5555

VL - 23

SP - 249

EP - 255

JO - JP Journal of Algebra, Number Theory and Applications

JF - JP Journal of Algebra, Number Theory and Applications

IS - 2

ER -

Elliptic curves with the real ℘-function

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

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