On the squareness of the discriminant of elliptic curves with an isogeny
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918318192984064 |
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| author | González-Jiménez, Enrique |
| author_facet | González-Jiménez, Enrique |
| contents | We establish a classification of the values of \( N \) for which an elliptic curve defined over \( \mathbb{Q} \) with square discriminant admits an \( N \)-isogeny. Furthermore, we determine the values of \( N \) for which two elliptic curves defined over \( \mathbb{Q} \), both possessing square discriminants, are \( N \)-isogenous. In both cases, we explicitly parametrize the corresponding \( j \)-invariants of the elliptic curves associated with these problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01384 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the squareness of the discriminant of elliptic curves with an isogeny González-Jiménez, Enrique Number Theory Algebraic Geometry Primary: 11G05, Secondary: 14H52 We establish a classification of the values of \( N \) for which an elliptic curve defined over \( \mathbb{Q} \) with square discriminant admits an \( N \)-isogeny. Furthermore, we determine the values of \( N \) for which two elliptic curves defined over \( \mathbb{Q} \), both possessing square discriminants, are \( N \)-isogenous. In both cases, we explicitly parametrize the corresponding \( j \)-invariants of the elliptic curves associated with these problems. |
| title | On the squareness of the discriminant of elliptic curves with an isogeny |
| topic | Number Theory Algebraic Geometry Primary: 11G05, Secondary: 14H52 |
| url | https://arxiv.org/abs/2602.01384 |