Computing integral points on hyperelliptic curves using quadratic chabauty

Jennifer S. Balakrishnan; Amnon Besser; J. Steffen Müller

doi:10.1090/mcom/3130

Computing integral points on hyperelliptic curves using quadratic chabauty

Jennifer S. Balakrishnan
, Amnon Besser
, J. Steffen Müller

Department of Mathematics

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

17 Scopus citations

Abstract

We give a method for the computation of integral points on a hyperelliptic curve of odd degree over the rationals whose genus equals the Mordell-Weil rank of its Jacobian. Our approach consists of a combination of the p-adic approximation techniques introduced in previous work with the Mordell-Weil sieve.

Original language	English
Pages (from-to)	1403-1434
Number of pages	32
Journal	Mathematics of Computation
Volume	86
Issue number	305
DOIs	https://doi.org/10.1090/mcom/3130
State	Published - 1 Jan 2017

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

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10.1090/mcom/3130

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title = "Computing integral points on hyperelliptic curves using quadratic chabauty",

abstract = "We give a method for the computation of integral points on a hyperelliptic curve of odd degree over the rationals whose genus equals the Mordell-Weil rank of its Jacobian. Our approach consists of a combination of the p-adic approximation techniques introduced in previous work with the Mordell-Weil sieve.",

author = "Balakrishnan, \{Jennifer S.\} and Amnon Besser and \{Steffen M{\"u}ller\}, J.",

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doi = "10.1090/mcom/3130",

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T1 - Computing integral points on hyperelliptic curves using quadratic chabauty

AU - Balakrishnan, Jennifer S.

AU - Besser, Amnon

AU - Steffen Müller, J.

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Y1 - 2017/1/1

N2 - We give a method for the computation of integral points on a hyperelliptic curve of odd degree over the rationals whose genus equals the Mordell-Weil rank of its Jacobian. Our approach consists of a combination of the p-adic approximation techniques introduced in previous work with the Mordell-Weil sieve.

AB - We give a method for the computation of integral points on a hyperelliptic curve of odd degree over the rationals whose genus equals the Mordell-Weil rank of its Jacobian. Our approach consists of a combination of the p-adic approximation techniques introduced in previous work with the Mordell-Weil sieve.

UR - https://www.scopus.com/pages/publications/85016198303

U2 - 10.1090/mcom/3130

DO - 10.1090/mcom/3130

M3 - Article

AN - SCOPUS:85016198303

SN - 0025-5718

VL - 86

SP - 1403

EP - 1434

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 305

ER -

Computing integral points on hyperelliptic curves using quadratic chabauty

Abstract

ASJC Scopus subject areas

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