Abbey Bourdon

activity

20152021

most citedAnatomy of torsion in the CM case

3 citations · 6 across the 3 of their papers we have counts for

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5 papers · 1 filter

math.NT2021

Sporadic points of odd degree on $X_{1} (N)$ coming from $Q$ -curves

Abbey Bourdon, Filip Najman

We say a closed point $x$ on a curve $C$ is sporadic if there are only finitely many points on $C$ of degree at most deg $(x)$ . In the case where $C$ is the modular curve $X_{1} (N)$ ,…

math.NT2020★ 3 cited

Odd degree isolated points on $X_{1} (N)$ with rational $j$ -invariant

Abbey Bourdon, David R. Gill, Jeremy Rouse +1

Let $C$ be a curve defined over a number field $k$ . We say a closed point $x \in C$ of degree $d$ is isolated if it does not belong to an infinite family of degree $d$ points parame…

math.NT2019

Torsion points and isogenies on CM elliptic curves

Abbey Bourdon, Pete L. Clark

Let $O$ be an order in the imaginary quadratic field $K$ . For positive integers $M ∣ N$ , we determine the least degree of an $O$ -CM point on the modular curv…

math.NT2018

On the level of modular curves that give rise to isolated $j$ -invariants

Abbey Bourdon, Ozlem Ejder, Yuan Liu +2

We say a closed point $x$ on a curve $C$ is sporadic if $C$ has only finitely many closed points of degree at most $deg (x)$ and that $x$ is isolated if it is not in…

math.NT2015★ 3 cited

Anatomy of torsion in the CM case

Abbey Bourdon, Pete L. Clark, Paul Pollack

Let $T_{CM} (d)$ denote the maximum size of a torsion subgroup of a CM elliptic curve over a degree $d$ number field. We initiate a systematic study of the asymptotic behav…

Sporadic points of odd degree on X1​(N) coming from Q-curves

Odd degree isolated points on X1​(N) with rational j-invariant

Torsion points and isogenies on CM elliptic curves

On the level of modular curves that give rise to isolated j-invariants

Anatomy of torsion in the CM case

Sporadic points of odd degree on $X_{1} (N)$ coming from $Q$ -curves

Odd degree isolated points on $X_{1} (N)$ with rational $j$ -invariant

On the level of modular curves that give rise to isolated $j$ -invariants