On the equation Y2 = X5 + k

Andrew Bremner

doi:10.1080/10586458.2008.10129039

On the equation Y² = X⁵ + k

Andrew Bremner

Mathematical and Statistical Sciences, School of (SoMSS)

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

3 Scopus citations

Abstract

We show that there are infinitely many nonisomorphic curves Y² = X⁵ + k, k ∈ ℤ, possessing at least twelve finite points for k > 0, and at least six finite points for k < 0. We also determine all rational points on the curve Y² = X⁵ − 7.

Original language	English (US)
Pages (from-to)	371-374
Number of pages	4
Journal	Experimental Mathematics
Volume	17
Issue number	3
DOIs	https://doi.org/10.1080/10586458.2008.10129039
State	Published - Jan 1 2008

Keywords

Elliptic curve
Fifth powers
Genus two curve

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1080/10586458.2008.10129039

Cite this

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title = "On the equation Y2 = X5 + k",

abstract = "We show that there are infinitely many nonisomorphic curves Y2 = X5 + k, k ∈ ℤ, possessing at least twelve finite points for k > 0, and at least six finite points for k < 0. We also determine all rational points on the curve Y2 = X5 − 7.",

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AB - We show that there are infinitely many nonisomorphic curves Y2 = X5 + k, k ∈ ℤ, possessing at least twelve finite points for k > 0, and at least six finite points for k < 0. We also determine all rational points on the curve Y2 = X5 − 7.

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KW - Genus two curve

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