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On elliptic curves with p-isogenies over quadratic fields
- Part of
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- Journal:
- Canadian Journal of Mathematics / Volume 75 / Issue 3 / June 2023
- Published online by Cambridge University Press:
- 07 June 2022, pp. 945-964
- Print publication:
- June 2023
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- Article
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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.
