M. Derickx

activity

20132026

most citedSporadic Cubic Torsion

44 citations · 175 across the 26 of their papers we have counts for

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Showing 2025Show all

7 papers · 1 filter

math.NT2025

Sporadic points on $X_{0} (N)$

Maarten Derickx, Filip Najman

We determine all integers $N$ for which the modular curve $X_{0} (N)$ admits a sporadic CM point (of any degree), as well as all $N$ for which $X_{0} (N)$ admits a sporadic point, whethe…

math.NT2025

Class groups of imaginary quadratic points on $X_{1} (16)$

Maarten Derickx

The main result is to show that if $K ≆ Q (- 15)$ is an imaginary quadratic field and $E$ is an elliptic curve over $K$ with a torsion point of order 16, then the…

math.AG2025

Morphisms on the modular curve $X_{0} (p)$ and degree $6$ points

Maarten Derickx, Petar Orlić

Let $p$ be a prime. We study non-constant morphisms $f : X_{0} (p)_{\to} Y$ , where $Y / Q$ is a curve of genus $\geq 2$ . We prove that for $p < 3000$ such an $f$ of degree $d>…

math.NT2025

Prime order torsion on elliptic curves over number fields. Part I: Asymptotics

Maarten Derickx, Michael Stoll

We study the asymptotics of the set $S (d)$ of possible prime orders of $K$ -rational points on elliptic curves over number fields $K$ of degree $d$ as $d$ tends to infinity. Assumin…

math.NT2025

Intermediate modular curves with infinitely many quartic points

Maarten Derickx, Petar Orlić

For every group ${\pm 1} \subseteq Δ \subseteq (Z / N Z)^{\times}$ , there exists an intermediate modular curve $X_{Δ} (N)$ . In this paper we determine all curves $X_{Δ} (N)$ wi…

math.NT2025

Contracting low degree points on curves

Maarten Derickx

The main result of this article is that all but finitely many points of small enough degree on a curve can be written as a pullback of a smaller degree point. The main theorem has…

math.NT2025

Modular curves $X_{0} (N)$ of density degree $5$

Maarten Derickx, Wontae Hwang, Daeyeol Jeon +1

We determine all modular curves $X_{0} (N)$ with density degree $5$ , i.e. all curves $X_{0} (N)$ with infinitely many points of degree $5$ and only finitely many points of degree $d\leq4…

Sporadic points on X0​(N)

Class groups of imaginary quadratic points on X1​(16)

Morphisms on the modular curve X0​(p) and degree 6 points

Prime order torsion on elliptic curves over number fields. Part I: Asymptotics

Intermediate modular curves with infinitely many quartic points

Contracting low degree points on curves

Modular curves X0​(N) of density degree 5

Sporadic points on $X_{0} (N)$

Class groups of imaginary quadratic points on $X_{1} (16)$

Morphisms on the modular curve $X_{0} (p)$ and degree $6$ points

Modular curves $X_{0} (N)$ of density degree $5$