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arXiv · 2403.01287

Towards a classification of $p^2$-discriminant ideal twins over number fields

Alyson Deines·Asimina S. Hamakiotes·Andreea Iorga·Changningphaabi Namoijam·Manami Roy·Lori D. Watson
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Abstract

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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Alyson Deines, Asimina S. Hamakiotes, Andreea Iorga, Changningphaabi Namoijam, Manami Roy, Lori D. Watson. 2024-03-02. Towards a classification of $p^2$-discriminant ideal twins over number fields. https://arxiv.org/abs/2403.01287

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