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On elliptic curves with p-isogenies over quadratic fields
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Michaud-Jacobs, Philippe (2023) On elliptic curves with p-isogenies over quadratic fields. Canadian Journal of Mathematics, 75 (3). pp. 945-964. doi:10.4153/S0008414X22000244 ISSN 0008-414X.
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Official URL: https://doi.org/10.4153/S0008414X22000244
Abstract
Let K be a number field. For which primes p does there exist an elliptic curve E/K admitting a K-rational p-isogeny? Although we have an answer to this question over the rationals, extending this to other number fields is a fundamental open problem in number theory. In this paper, we study this question in the case that K is a quadratic field, subject to the assumption that E is semistable at the primes of K above p. We prove results both for families of quadratic fields and for specific quadratic fields.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Canadian Journal of Mathematics | ||||||||
Publisher: | Cambridge University Press | ||||||||
ISSN: | 0008-414X | ||||||||
Official Date: | June 2023 | ||||||||
Dates: |
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Volume: | 75 | ||||||||
Number: | 3 | ||||||||
Page Range: | pp. 945-964 | ||||||||
DOI: | 10.4153/S0008414X22000244 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Copyright Holders: | © The Canadian Mathematical Society, 2022 | ||||||||
Date of first compliant deposit: | 8 June 2022 | ||||||||
Date of first compliant Open Access: | 1 July 2022 | ||||||||
RIOXX Funder/Project Grant: |
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