Geodesic
On elliptic curves with p-isogenies over quadratic fields
Canadian journal of mathematics, Tome 75 (2023) no. 3, pp. 945-964

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DOI

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.
DOI : 10.4153/S0008414X22000244
Mots-clés : Elliptic curve, isogeny, irreducibility, Galois representation, quadratic field, modular curve 
Michaud-Jacobs, Philippe. On elliptic curves with p-isogenies over quadratic fields. Canadian journal of mathematics, Tome 75 (2023) no. 3, pp. 945-964. doi: 10.4153/S0008414X22000244
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