M. Derickx

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20242026

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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.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.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…

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

Sporadic points on X0​(N)

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

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

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

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

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