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Isogenous elliptic curves have the same conductor but not necessarily the same minimal discriminant ideal. In this article, we explicitly classify all \(p^2\) -isogenous elliptic curves defined over a number field with the same minimal discriminant ideal for odd prime p where \(X_0(p^2)\) has genus 0, i.e., \(p = 3\) or 5. As a consequence, we give a list of all \(p^2\) -isogenous discriminant (ideal) twins over \(\mathbb {Q}\) for such p.

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Towards a Classification of  \(p^2\) -Discriminant Ideal Twins Over Number Fields

  • 会议论文

  • 出版模式：

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  • 发表日期：

    2026年

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  • Alyson Deines,
  • Asimina S. Hamakiotes,
  • Andreea Iorga,
  • Changningphaabi Namoijam,
  • Manami Roy,
  • Lori D. Watson

摘要

Isogenous elliptic curves have the same conductor but not necessarily the same minimal discriminant ideal. In this article, we explicitly classify all \(p^2\) -isogenous elliptic curves defined over a number field with the same minimal discriminant ideal for odd prime p where \(X_0(p^2)\) has genus 0, i.e., \(p = 3\) or 5. As a consequence, we give a list of all \(p^2\) -isogenous discriminant (ideal) twins over \(\mathbb {Q}\) for such p.