John Cullinan

collaborators

4 papers

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

Tamagawa Numbers of Elliptic Curves with an $ℓ$ -isogeny

Alexander Barrios, John Cullinan

Let $ℓ$ be an odd prime, and suppose $E$ is an elliptic curve defined over the rational numbers $Q$ . If $E$ has an $ℓ$ -torsion point, then there has been significant…

math.RT2024

Unisingular Specht Modules

John Cullinan

Let $G$ be a finite group and $ρ:G \to \GL(V)$ a finite dimensional representation of $G$ . We say that $ρ$ is unisingular if $det (1 - ρ (g)) = 0$ for all $g \in G$ . Building on previ…

math.RT2024

On the modular Plesken Lie algebra

John Cullinan

Let G be a finite group. The Plesken Lie algebra L[G] is a subalgebra of the complex group algebra C[G] and admits a direct-sum decomposition into simple Lie algebras based on the…

The probability of isomorphic group structures of isogenous elliptic curves over finite fields

Tamagawa Numbers of Elliptic Curves with an ℓ-isogeny

Unisingular Specht Modules

On the modular Plesken Lie algebra

Tamagawa Numbers of Elliptic Curves with an $ℓ$ -isogeny