On the torsion growth in quadratic number fields for elliptic curves defined over the rationals
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911496998486016 |
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| author | Arias-de-Reyna, Sara Pineda-Martín, Miguel Tornero, José M. |
| author_facet | Arias-de-Reyna, Sara Pineda-Martín, Miguel Tornero, José M. |
| contents | Given an elliptic curve defined over the field of rational numbers, it is known how its torsion subgroup may grow when we make a base change to a quadratic number field. In this paper we consider the inverse question: if we have the elliptic curve defined over the rationals and we know how the torsion subgroup grows, what can we say about the field? Our main result gives an explicit relationship between the primes dividing the conductor of the curve and the conductor of the extension as a first approach to a better understanding of this problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03286 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the torsion growth in quadratic number fields for elliptic curves defined over the rationals Arias-de-Reyna, Sara Pineda-Martín, Miguel Tornero, José M. Number Theory 11G05, 14H52 Given an elliptic curve defined over the field of rational numbers, it is known how its torsion subgroup may grow when we make a base change to a quadratic number field. In this paper we consider the inverse question: if we have the elliptic curve defined over the rationals and we know how the torsion subgroup grows, what can we say about the field? Our main result gives an explicit relationship between the primes dividing the conductor of the curve and the conductor of the extension as a first approach to a better understanding of this problem. |
| title | On the torsion growth in quadratic number fields for elliptic curves defined over the rationals |
| topic | Number Theory 11G05, 14H52 |
| url | https://arxiv.org/abs/2504.03286 |