On non-congruent numbers with 1 modulo 4 prime factors

2012/08/10 by Yi Ouyang, Ouyang, Yi, Shenxing Zhang +1
Mathematics · #11G05 (Primary) 11D25 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11D25 #msc:11G05

paper · pdf · doi:10.48550/arxiv.1208.2149

arxiv created 2012/08/10 · openalex publication_date 2012/08/10 · arxiv updated 2012/08/13 · openalex created_date 2019/03/02 · openalex updated_date 2026/07/28

Abstract

In this paper, we use the 2-decent method to find a series of odd non-congruent numbers ≡1\pmod 8 whose prime factors are ≡1\pmod4 such that the congruent elliptic curves have second lowest Selmer groups, which includes Li and Tian's result (Li and Tian, 2000) as special cases.

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