Abbey Bourdon

activity

20132026

most citedTorsion points and Galois representations on CM elliptic curves

27 citations · 44 across the 10 of their papers we have counts for

collaborators

15 papers

math.NT2026

On the Finiteness of Isolated $j$ -invariants for $X_{1} (N)$

Abbey Bourdon

Characterizing isolated points on the modular curve $X_{1} (N)$ is a key obstruction to classifying all points of a fixed degree. These points do not lie in infinite parameterized fam…

math.NT2025

Rational isolated $j$ -invariants from $X_{1} (ℓ^{n})$ and $X_{0} (ℓ^{n})$

Abbey Bourdon, Özlem Ejder

Let $ℓ$ and $n$ be positive integers with $ℓ$ prime. The modular curves $X_{1} (ℓ^{n})$ and $X_{0} (ℓ^{n})$ are algebraic curves over $Q$ whose non-cuspidal points param…

math.NT2024

Uniform polynomial bounds on torsion from rational geometric isogeny classes

Abbey Bourdon, Tyler Genao

In 1996, Merel showed there exists a function $B : Z^{+} \to Z^{+}$ such that for any elliptic curve $E / F$ defined over a number field of degree $d$ , one h…

math.NT2024

Minimal torsion curves in geometric isogeny classes

Abbey Bourdon, Nina Ryalls, Lori D. Watson

In this paper, we introduce the study of minimal torsion curves within a fixed geometric isogeny class. For a $Q$ -isogeny class $E$ of elliptic curves…

math.NT2023★ 1 cited

Towards a classification of isolated $j$ -invariants

Abbey Bourdon, Sachi Hashimoto, Timo Keller +5

We develop an algorithm to test whether a non-CM elliptic curve $E / Q$ gives rise to an isolated point of any degree on any modular curve of the form $X_{1} (N)$ . This builds…

math.NT2021

Torsion for CM elliptic curves defined over number fields of degree 2p

Abbey Bourdon, Holly Paige Chaos

For a prime number p, we characterize the groups that may arise as torsion subgroups of an elliptic curve with complex multiplication defined over a number field of degree 2p. In p…