Families of non-congruent numbers with arbitrarily many prime factors

DOI10.1016/j.jnt.2012.07.011zbMath1278.11063OpenAlexW1979903565MaRDI QIDQ1762312

Lindsey Reinholz, Blair K. Spearman, Qiduan Yang

Publication date: 23 November 2012

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2012.07.011

zbMATH Keywords

elliptic curverankcongruent numbersnon-congruent numbers

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05)

Related Items (8)

Some new families of non-congruent numbers ⋮ Families of non-congruent numbers with odd prime factors of the form \(8k + 3\) ⋮ Families of non-$\theta $-congruent numbers with arbitrarily many prime factors ⋮ An extension theorem for generating new families of non-congruent numbers ⋮ On the extension of even families of non-congruent numbers ⋮ Families of even non-congruent numbers with prime factors in each odd congruence class modulo eight ⋮ The non-congruent numbers via Monsky’s formula ⋮ Adaptation of Monsky matrices for 𝜃-congruent numbers

Cites Work

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• Non-congruent numbers with arbitrarily many prime factors congruent to 3 modulo 8
• Mock Heegner points and congruent numbers
• The size of Selmer groups for the congruent number problem. II. With an appendix by P. Monsky.
• On Congruent Numbers with Three Prime Factors
• Sur certaines hypothèses concernant les nombres premiers
• Non-congruent numbers, odd graphs and the Birch-Swinnerton-Dyer conjecture

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