M. Derickx

activity

20132026

most citedSporadic Cubic Torsion

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

collaborators

28 papers

math.NT2026

Semi-stable models, local heights and quadratic Chabauty for $X_{0} (N)^{*}$

Nikola Adžaga, Maarten Derickx, Timo Keller

Quadratic Chabauty computations for $X_{0} (N)^{*}$ are complicated by local height contributions at primes of bad reduction. For squarefree $N$ , we explain a strategy for constructing…

math.NT2026

$D$ -elliptic modular curves $X_{0} (N)$

Maarten Derickx, Daeyeol Jeon, Yongjae Kwon +1

We present a method for determining whether there exists a degree $D$ rational map from $X_{0} (N)$ to some elliptic curve $E / Q$ . Moreover, we explain how to obtain a quadrat…

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

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.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…

math.NT2024★ 1 cited

Classification of torsion of elliptic curves over quartic fields

Maarten Derickx, Filip Najman

Let $E$ be an elliptic curve over a quartic field $K$ . By the Mordell-Weil theorem, $E (K)$ is a finitely generated group. We determine all the possibilities for the torsion group $…

math.NT2024★ 1 cited

Large degree primitive points on curves

Maarten Derickx

A number field $K$ is called primitive if $Q$ and $K$ are the only subfields of $K$ . Let $X$ be a nice curve over $Q$ of genus $g$ . A point $P$ of degree $d$ on $X$ …

math.NT2024

Torsion subgroups of elliptic curves over quadratic fields and a conjecture of Granville

Barinder S. Banwait, Maarten Derickx

We study the problem of determining the groups that can arise as the torsion subgroup of an elliptic curve over a fixed quadratic field, building on work of Kamienny-Najman, Krumm,…

math.NT2023★ 3 cited

Modular curves $X_{0} (N)$ with infinitely many quartic points

Maarten Derickx, Petar Orlić

We determine all modular curves $X_{0} (N)$ with infinitely many quartic points. To do this, we define a pairing that induces a quadratic form representing all possible degrees of a r…

math.NT2023

Hyperelliptic and trigonal modular curves in characteristic $p$

Maarten Derickx, Filip Najman

Let $X_{Δ} (N)$ be an intermediate modular curve of level $N$ , meaning that there exist (possibly trivial) morphisms $X_{1} (N) \to X_{Δ} (N) \to X_{0} (N)$ . For all such interm…

math.NT2023

Towards strong uniformity for isogenies of prime degree

Barinder S. Banwait, Maarten Derickx

Let $E$ be an elliptic curve over a number field $k$ of degree $d$ that admits a $k$ -rational isogeny of prime degree $p$ . We study the question of finding a uniform bound on $p$ t…

math.NT2022

Explicit isogenies of prime degree over number fields

Barinder S. Banwait, Maarten Derickx

We provide an explicit and algorithmic version of a theorem of Momose classifying isogenies of prime degree of elliptic curves over number fields, which we implement in Sage and PA…

math.NT2021★ 1 cited

Elliptic curves with a point of order 13 defined over cyclic cubic fields

Peter Bruin, Maarten Derickx, Michael Stoll

We show that there is essentially a unique elliptic curve $E$ defined over a cubic Galois extension $K$ of $Q$ with a $K$ -rational point of order 13 and such that $E$ is no…

math.NT2020★ 44 cited

Sporadic Cubic Torsion

Maarten Derickx, Anastassia Etropolski, Mark van Hoeij +2

Let $K$ be a number field, and let $E / K$ be an elliptic curve over $K$ . The Mordell--Weil theorem asserts that the $K$ -rational points $E (K)$ of $E$ form a finitely generated abeli…

math.NT2020★ 19 cited

Computing classical modular forms

Alex J. Best, Jonathan Bober, Andrew R. Booker +8

We discuss practical and some theoretical aspects of computing a database of classical modular forms in the L-functions and Modular Forms Database (LMFDB).

math.NT2019★ 21 cited

Elliptic Curves over Totally Real Cubic Fields are Modular

Maarten Derickx, Filip Najman, Samir Siksek

We prove that all elliptic curves defined over totally real cubic fields are modular. This builds on previous work of Freitas, Le Hung and Siksek, who proved modularity of elliptic…

math.NT2018★ 10 cited

Torsion of elliptic curves over cyclic cubic fields

Maarten Derickx, Filip Najman

We determine all the possible torsion groups of elliptic curves over cyclic cubic fields, over non-cyclic totally real cubic fields and over complex cubic fields.

math.NT2018★ 3 cited

Groups of generalized $G$ -type and applications to torsion subgroups of rational elliptic curves over infinite extensions of $Q$

Harris B. Daniels, Maarten Derickx, Jeffrey Hatley

Recently there has been much interest in studying the torsion subgroups of elliptic curves base-extended to infinite extensions of $Q$ . In this paper, given a finite group…

Semi-stable models, local heights and quadratic Chabauty for X0​(N)∗

D-elliptic modular curves X0​(N)

Rational points on modular curves: parameterization and geometric explanations

Computing class groups and gonalities of algebraic curves over finite fields

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

Classification of torsion of elliptic curves over quartic fields

Large degree primitive points on curves

Torsion subgroups of elliptic curves over quadratic fields and a conjecture of Granville

Modular curves X0​(N) with infinitely many quartic points

Hyperelliptic and trigonal modular curves in characteristic p

Towards strong uniformity for isogenies of prime degree

Explicit isogenies of prime degree over number fields

Elliptic curves with a point of order 13 defined over cyclic cubic fields

Sporadic Cubic Torsion

Computing classical modular forms

Elliptic Curves over Totally Real Cubic Fields are Modular

Torsion of elliptic curves over cyclic cubic fields

Groups of generalized G-type and applications to torsion subgroups of rational elliptic curves over infinite extensions of Q

Semi-stable models, local heights and quadratic Chabauty for $X_{0} (N)^{*}$

$D$ -elliptic modular curves $X_{0} (N)$

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 $5$

Modular curves $X_{0} (N)$ with infinitely many quartic points

Hyperelliptic and trigonal modular curves in characteristic $p$

Groups of generalized $G$ -type and applications to torsion subgroups of rational elliptic curves over infinite extensions of $Q$