Filip Najman

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20232025

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math.NT2025

Quadratic points on modular curves $X_{0} (N)$ for $N \leq 100$

Filip Najman, Ivan Novak

We determine the quadratic points on the modular curves $X_{0} (N)$ for $N \leq 100$ for which this has not been previously done, namely the cases $$N\in\{66,70,78,82,84,86,87,88,90,96…

math.NT2024

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.NT2023

Towards a classification of isolated $j$ -invariants

Abbey Bourdon, Sachi Hashimoto, Timo Keller +5

We develop an algorithm to test whether a non-CM elliptic curve $E / Q$ gives rise to an isolated point of any degree on any modular curve of the form $X_{1} (N)$ . This builds…

Quadratic points on modular curves X0​(N) for N≤100

Classification of torsion of elliptic curves over quartic fields

Towards a classification of isolated j-invariants

Quadratic points on modular curves $X_{0} (N)$ for $N \leq 100$

Towards a classification of isolated $j$ -invariants