Filip Najman

activity

20102026

most citedGrowth of torsion groups of elliptic curves upon base change

38 citations · 186 across the 31 of their papers we have counts for

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42 papers · 1 filter

math.NT2026

Classification of torsion of elliptic curves over quintic fields

Filip Najman

We determine all the groups that appear as the torsion group of an elliptic curve over a quintic number field. Apart from the groups that already occur infinitely often, which were…

math.NT2026

Torsion groups of elliptic curves that appear infinitely often over septic, octic and nonic fields

Filip Najman, Marin Varivoda

We determine the sets $Φ^{\infty} (n)$ of abelian groups that appear as torsion groups of infinitely many elliptic curves, up to $\overline \Q$-isomorphism, over number fields of degr…

math.NT2023

On $r$ -isogenies over $Q (ζ_{r})$ of elliptic curves with rational $j$ -invariants

Filip Najman

The main goal of this paper is to determine for which prime numbers $r \geq 3$ can an elliptic curve~ $E$ defined over $Q$ have an $r$ -isogeny over $Q (ζ_{r})$ . We study…

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★ 7 cited

Computing quadratic points on modular curves $X_{0} (N)$

Nikola Adžaga, Timo Keller, Philippe Michaud-Jacobs +3

In this paper we improve on existing methods to compute quadratic points on modular curves and apply them to successfully find all the quadratic points on all modular curves $X_0(N…

math.NT2022★ 4 cited

Gonality of the modular curve $X_{0} (N)$

Filip Najman, Petar Orlić

In this paper we determine the $Q$ -gonalities of the modular curves $X_{0} (N)$ for all $N < 145$ . We determine the $C$ -gonality of many of these curves and the $\mathbb…

math.NT2022

Two results on $x^{r} + y^{r} = d z^{p}$

Nuno Freitas, Filip Najman

This note proves two theorems regarding Fermat-type equation $x^{r} + y^{r} = d z^{p}$ where $r \geq 5$ is a prime. Our main result shows that, for infinitely many integers~ $d$ , the previ…

math.NT2022★ 1 cited

Cyclic isogenies of elliptic curves over fixed quadratic fields

Barinder S. Banwait, Filip Najman, Oana Padurariu

Building on Mazur's 1978 work on prime degree isogenies, Kenku determined in 1981 all possible cyclic isogenies of elliptic curves over $Q$ . Although more than 40 years ha…

math.NT2021

Quadratic points on bielliptic modular curves

Filip Najman, Borna Vukorepa

Bruin and Najman, Ozman and Siksek, and Box described all the quadratic points on the modular curves of genus $2 \leq g (X_{0} (n)) \leq 5$ . Since all the hyperelliptic curves $X_{0} (n)$ …

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

Splitting of primes in number fields generated by points on some modular curves

Filip Najman, Antonela Trbović

We study the splitting of primes in number fields generated by points on modular curves. Momose was the first to notice that quadratic points on $X_{1} (n)$ generate quadratic fields…

math.NT2020★ 7 cited

Counting elliptic curves with prescribed level structures over number fields

Peter Bruin, Filip Najman

Harron and Snowden counted the number of elliptic curves over $Q$ up to height $X$ with torsion group $G$ for each possible torsion group $G$ over $Q$ . In this pa…

math.NT2020

$Q$ -curves over odd degree number fields

John Cremona, Filip Najman

By reformulating and extending results of Elkies, we prove some results on $Q$ -curves over number fields of odd degree. We show that, over such fields, the only prime isoge…

math.NT2020★ 3 cited

Irreducibility of mod p Galois representations of elliptic curves with multiplicative reduction over number fields

Filip Najman, George C. Turcas

In this note we prove that for every integer $d \geq 1$ , there exists an explicit constant $B_{d}$ such that the following holds. Let $K$ be a number field of degree $d$ , let $q > \m…

math.NT2019★ 5 cited

An algorithm for determining torsion growth of elliptic curves

Enrique González-Jiménez, Filip Najman

We present a fast algorithm that takes as input an elliptic curve defined over $Q$ and an integer $d$ and returns all the number fields $K$ of degree $d^{'}$ dividing $d$ such…

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

Torsion groups of elliptic curves over the $Z_{p}$ -extensions of $Q$

Michael Chou, Harris B. Daniels, Ivan Krijan +1

We determine, for an elliptic curve $E / Q$ and for all $p$ , all the possible torsion groups $E (Q_{\infty, p})_{t or s}$ , where $Q_{\infty, p}$ is the $\mathbb…

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★ 1 cited

Torsion of $\Q$-curves over quadratic fields

Samuel Le Fourn, Filip Najman

We find all the possible torsion groups of $\Q$-curves over quadratic fields and determine which groups appear finitely and which appear infinitely often.

math.NT2016★ 38 cited

Growth of torsion groups of elliptic curves upon base change

Enrique González-Jiménez, Filip Najman

We study how the torsion of elliptic curves over number fields grows upon base change, and in particular prove various necessary conditions for torsion growth. For a number field $…

math.NT2016

Fields of definition of elliptic curves with prescribed torsion

Peter Bruin, Filip Najman

We prove that all elliptic curves over quadratic fields with a subgroup isomorphic to $C_{16}$ , as well as all elliptic curves over cubic fields with a subgroup isomorphic to $C_2\…

math.NT2016

Tamagawa Numbers of elliptic curves with $C_{13}$ torsion over quadratic fields

Filip Najman

Let $E$ be an elliptic curve over a number field $K$ , $c_{v}$ the Tamagawa number of $E$ at $v$ , and let $c_{E} = \prod_{v} c_{v}$ . Lorenzini proved that $v_{13} (c_{E})$ is postive for all el…

math.NT2015★ 19 cited

Torsion subgroups of rational elliptic curves over the compositum of all cubic fields

Harris B. Daniels, Alvaro Lozano-Robledo, Filip Najman +1

Let $E / Q$ be an elliptic curve and let $Q (3^{\infty})$ be the compositum of all cubic extensions of $Q$ . In this article we show that the torsion subgroup…

math.NT2015★ 2 cited

Isogenies of non-CM elliptic curves with rational $j$ -invariants over number fields

Filip Najman

We unconditionally determine $I_\Q(d)$, the set of possible prime degrees of cyclic $K$ -isogneies of elliptic curves with $\Q$-rational $j$ -invariants and without complex multiplic…

Classification of torsion of elliptic curves over quintic fields

Torsion groups of elliptic curves that appear infinitely often over septic, octic and nonic fields

On r-isogenies over Q(ζr​) of elliptic curves with rational j-invariants

Hyperelliptic and trigonal modular curves in characteristic p

Computing quadratic points on modular curves X0​(N)

Gonality of the modular curve X0​(N)

Two results on xr+yr=dzp

Cyclic isogenies of elliptic curves over fixed quadratic fields

Quadratic points on bielliptic modular curves

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

Splitting of primes in number fields generated by points on some modular curves

Counting elliptic curves with prescribed level structures over number fields

Q-curves over odd degree number fields

Irreducibility of mod p Galois representations of elliptic curves with multiplicative reduction over number fields

An algorithm for determining torsion growth of elliptic curves

Elliptic Curves over Totally Real Cubic Fields are Modular

Torsion groups of elliptic curves over the Zp​-extensions of Q

Torsion of elliptic curves over cyclic cubic fields

Torsion of $\Q$-curves over quadratic fields

Growth of torsion groups of elliptic curves upon base change

Fields of definition of elliptic curves with prescribed torsion

Tamagawa Numbers of elliptic curves with C13​ torsion over quadratic fields

Torsion subgroups of rational elliptic curves over the compositum of all cubic fields

Isogenies of non-CM elliptic curves with rational j-invariants over number fields

On $r$ -isogenies over $Q (ζ_{r})$ of elliptic curves with rational $j$ -invariants

Hyperelliptic and trigonal modular curves in characteristic $p$

Computing quadratic points on modular curves $X_{0} (N)$

Gonality of the modular curve $X_{0} (N)$

Two results on $x^{r} + y^{r} = d z^{p}$

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

$Q$ -curves over odd degree number fields

Torsion groups of elliptic curves over the $Z_{p}$ -extensions of $Q$

Tamagawa Numbers of elliptic curves with $C_{13}$ torsion over quadratic fields

Isogenies of non-CM elliptic curves with rational $j$ -invariants over number fields