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math.NT2026
A mod determinant criterion for Cohen--Lenstra convergence of random -adic matrices with prescribed zero patterns
Hyungmin Jang, Nathan Kaplan, Jungin Lee +1
We study the distribution of cokernels of Haar-random matrices over the -adic integers with prescribed zero patterns, motivated by the Cohen--Lenstra heuristics. A central featu…
math.NT2025
The probability of isomorphic group structures of isogenous elliptic curves over finite fields
John Cullinan, Nathan Kaplan
Let l be a prime number and let E and E' be l-isogenous elliptic curves defined over Q. In this paper we determine the proportion of primes p for which E(F_p) is isomorphic to E'(F…
math.NT2024
The probability of non-isomorphic group structures of isogenous elliptic curves in finite field extensions, II
John Cullinan, Shanna Dobson, Linda Frey +5
Let and be 2-isogenous elliptic curves over $\Q$. Following \cite{ck}, we call a good prime \emph{anomalous} if $E(\F_p) \simeq E'(\F_p)$ but $E(\F_{p^2}) \not \simeq…