Families of even non-congruent numbers with prime factors in each odd congruence class modulo eight

DOI10.1142/S1793042118500422zbMath1429.11108WikidataQ114071994 ScholiaQ114071994MaRDI QIDQ4609568

Qiduan Yang, Blair K. Spearman, Lindsey Reinholz

Publication date: 4 April 2018

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

zbMATH Keywords

elliptic curveranknon-congruent numbercongruent number

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05)

Related Items (4)

Families of even noncongruent numbers with arbitrarily many pairs of prime factors ⋮ Families of non-congruent numbers with odd prime factors of the form \(8k + 3\) ⋮ On the extension of even families of non-congruent numbers ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On non-congruent numbers with 1 modulo 4 prime factors
• Non-congruent numbers with arbitrarily many prime factors congruent to 3 modulo 8
• A note on the Selmer group of the elliptic curve \(y^ 2=x^ 3+Dx\).
• New series of odd non-congruent numbers
• A classical Diophantine problem and modular forms of weight \(3/2\)
• The size of Selmer groups for the congruent number problem. II. With an appendix by P. Monsky.
• An extension theorem for generating new families of non-congruent numbers
• Families of non-congruent numbers with arbitrarily many prime factors
• On elliptic curves \(y^{2} = x^{3}-n^{2}x\) with rank zero
• On second 2-descent and non-congruent numbers
• The Arithmetic of Elliptic Curves
• Non-congruent numbers, odd graphs and the Birch-Swinnerton-Dyer conjecture
• On the prime factors of non-congruent numbers

This page was built for publication: Families of even non-congruent numbers with prime factors in each odd congruence class modulo eight