Integral points on a certain family of elliptic curves

Shabnam Akhtari

doi:10.5802/jtnb.905

Shabnam Akhtari ¹

¹ Fenton Hall University of Oregon Eugene, OR 97403-1222 USA

Journal de théorie des nombres de Bordeaux, Volume 27 (2015) no. 2, pp. 353-373.

Abstract
Résumé

The Thue-Siegel method is used to obtain an upper bound for the number of primitive integral solutions to a family of quartic Thue’s inequalities. This will provide an upper bound for the number of integer points on a family of elliptic curves with j-invariant equal to $1728$ .

Nous utilisons la méthode de Thue-Siegel pour obtenir une borne supérieure du nombre de solutions entières primitives d’une famille d’inégalités quartic de Thue. Cela permet de donner une borne supérieure du nombre de points entiers pour une famille de courbes elliptiques d’invariant $j$ égal à $1728$ .

MR

DOI: 10.5802/jtnb.905

Classification: 11D25, 11J86
Keywords: Elliptic Curvers, Quartic Thue equations

Author's affiliations:

Shabnam Akhtari ¹

¹ Fenton Hall University of Oregon Eugene, OR 97403-1222 USA

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Shabnam Akhtari. Integral points on a certain family of elliptic curves. Journal de théorie des nombres de Bordeaux, Volume 27 (2015) no. 2, pp. 353-373. doi : 10.5802/jtnb.905. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.905/

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