Towards a classification of $p^2$-discriminant ideal twins over number fields
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912044559630336 |
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| author | Deines, Alyson Hamakiotes, Asimina S. Iorga, Andreea Namoijam, Changningphaabi Roy, Manami Watson, Lori D. |
| author_facet | Deines, Alyson Hamakiotes, Asimina S. Iorga, Andreea Namoijam, Changningphaabi Roy, Manami Watson, Lori D. |
| contents | 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 $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01287 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards a classification of $p^2$-discriminant ideal twins over number fields Deines, Alyson Hamakiotes, Asimina S. Iorga, Andreea Namoijam, Changningphaabi Roy, Manami Watson, Lori D. Number Theory 11G05, 14K02, 14H10, 14H52 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 $p$. |
| title | Towards a classification of $p^2$-discriminant ideal twins over number fields |
| topic | Number Theory 11G05, 14K02, 14H10, 14H52 |
| url | https://arxiv.org/abs/2403.01287 |