Ivan Novak

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20242026

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math.NT2026

Isogeny graphs of elliptic curves in characteristic zero

Alexander J. Barrios, Enrique González-Jiménez, Ivan Novak

For an elliptic curve $E$ defined over a field $K$ of characteristic $0$ with $End_{K} E ≅ Z$ , we classify which isogeny graphs $G (E / K)$ can…

math.NT2025

Number of $K$ -rational points with given $j$ -invariant on modular curves

Ivan Novak

In this article, we study how to compute the number of $K$ -rational points with a given $j$ -invariant on an arbitrary modular curve. As an application, for each positive integer $n…

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.NT2025

Torsion of $Q$ -curves over number fields of small odd prime degree

Ivan Novak

We determine all groups which occur as torsion subgroups of $Q$ -curves defined over number fields of degrees $3$ , $5$ and $7$ . In particular, we prove that every torsion su…

math.NT2024

Degrees of isogenies over prime degree number fields of non-CM elliptic curves with rational $j$ -invariant

Ivan Novak

We determine all possible degrees of cyclic isogenies of non-CM elliptic curves with rational $j$ -invariant over number fields of degree $p$ , where $p$ is an odd prime. The questio…

Isogeny graphs of elliptic curves in characteristic zero

Number of K-rational points with given j-invariant on modular curves

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

Torsion of Q-curves over number fields of small odd prime degree

Degrees of isogenies over prime degree number fields of non-CM elliptic curves with rational j-invariant

Number of $K$ -rational points with given $j$ -invariant on modular curves

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

Torsion of $Q$ -curves over number fields of small odd prime degree

Degrees of isogenies over prime degree number fields of non-CM elliptic curves with rational $j$ -invariant