On the extension of even families of non-congruent numbers

DOI10.4171/RSMUP/105OpenAlexW4312078624MaRDI QIDQ2697592

Lindsey Reinholz, Qiduan Yang

Publication date: 12 April 2023

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/rsmup/105

zbMATH Keywords

elliptic curveranknon-congruent numbercongruent number

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05)

Cites Work

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• 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
• The size of Selmer groups for the congruent number problem. II. With an appendix by P. Monsky.
• On the Birch-Swinnerton-Dyer conjecture of elliptic curves \(E_D:y^2 = x^3-D^2 x\)
• Some new families of non-congruent numbers
• 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
• Congruent elliptic curves with non-trivial Shafarevich-Tate groups
• On second 2-descent and non-congruent numbers
• Families of even non-congruent numbers with prime factors in each odd congruence class modulo eight
• Non-congruent numbers, odd graphs and the Birch-Swinnerton-Dyer conjecture
• On the prime factors of non-congruent numbers

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