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The probability of non-isomorphic group structures of isogenous elliptic curves in finite field extensions, II
Published 11 Jan 2024 in math.NT | (2401.06250v1)
Abstract: Let $E$ and $E'$ be 2-isogenous elliptic curves over $\Q$. Following \cite{ck}, we call a good prime $p$ \emph{anomalous} if $E(\F_p) \simeq E'(\F_p)$ but $E(\F_{p2}) \not \simeq E'(\F_{p2})$. Our main result is an explicit formula for the proportion of anomalous primes for any such pair of elliptic curves. We consider both the CM case and the non-CM case.
- Cullinan, John. A remark on the group structure of elliptic curves in towers of finite fields. New York J. Math. 24 (2018) 857-865.
- Cullinan, John. A remark on the group structure of 2-isogenous elliptic curves in towers of finite fields. New York J. Math. (2020) 26 207-217.
- Lang, Serge. Elliptic Functions. Graduate Texts in Mathematics. Vol. 112. With an appendix by J. Tate (Second edition of 1973 original ed.). New York: Springer-Verlag.
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