M. Derickx

activity

20242026

collaborators

12 papers

math.NT2026

Computing class groups and gonalities of algebraic curves over finite fields

Maarten Derickx, Kenji Terao

We give practical algorithms for computing the divisor class group and the gonality of a curve over a finite field, achieving several orders of magnitude speedup over existing meth…

math.NT2026

Rational points on modular curves: parameterization and geometric explanations

Maarten Derickx, Sachi Hashimoto, Filip Najman +1

We show that, conditional on Zywina's effective version of the Serre uniformity conjecture, there is a natural way to parameterize non-CM $Q$ -rational points on all modula…

math.NT2026

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…

math.AG2026

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

Maarten Derickx, Petar OrliÄ

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

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…

Computing class groups and gonalities of algebraic curves over finite fields

Rational points on modular curves: parameterization and geometric explanations

Modular curves X0​(N) of density degree 5

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

Sporadic points on X0​(N)

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

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

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

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

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