One Integer Point on Some Elliptic Curve to Have Rank 1

Walsh proved a necessary condition for some curves of the form y2=x3-px, with p is a prime, to have Mordell - Weil rank 1. In this paper, we extend Walshs result to show that some curves have Mordell-Weil rank 1.

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Publication Details

Journal
Indian Journal of Advanced Mathematics
Published
2026-10-26
DOI
https://doi.org/10.54105/ijam.a1245.06010426
Primary Topic
Algebraic Geometry and Number Theory
Type
article
Field-Weighted Citation Impact
0.00
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article

One Integer Point on Some Elliptic Curve to Have Rank 1

Hasan Sankari, Ahmad Abdo, Safwan Aouira
Indian Journal of Advanced Mathematics
Algebraic Geometry and Number Theory
article

One Integer Point on Some Elliptic Curve to Have Rank 1

Hasan Sankari, Ahmad Abdo, Safwan Aouira
article en

Abstract

Walsh proved a necessary condition for some curves of the form y2=x3-px, with p is a prime, to have Mordell - Weil rank 1. In this paper, we extend Walshs result to show that some curves have Mordell-Weil rank 1.

Indian Journal of Advanced MathematicsVol. 6(2)
University of Aleppo (SY), Latakia University (SY)
Openalex Percentile: Top 8%
Algebraic Geometry and Number Theory
DOIOpen Access PDFOpenAlex
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One Integer Point on Some Elliptic Curve to Have Rank 1 — Hasan Sankari, Ahmad Abdo, et al. · Indian Journal of Advanced Mathematics (2026) | TGRS Research Map | TGRS