Filip Najman

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20232026

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math.NT2026

Rational torsion on simple genus two Jacobians

Jennifer S. Balakrishnan, Filip Najman, Ari Shnidman +1

We exhibit new subgroups of rational torsion points in geometrically simple Jacobians of genus-two curves over $Q$ . The largest group, which has order 96 and invariants [2,…

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.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.NT2023

Quadratic points on $X_{0} (163)$

Philippe Michaud-Jacobs, Filip Najman

We determine all the quadratic points on the genus $13$ modular curve $X_{0} (163)$ , thus completing the answer to a recent question of Banwait, the second-named author, and Padurariu…

Rational torsion on simple genus two Jacobians

Rational points on modular curves: parameterization and geometric explanations

Sporadic points on X0​(N)

Quadratic points on X0​(163)

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

Quadratic points on $X_{0} (163)$