Petar Orlić

activity

20222026

X_{0} (N)

4 citations · 7 across the 10 of their papers we have counts for

collaborators

11 papers

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.NT2025

Tetragonal modular quotients of $X_{0} (N)$

Petar Orlić

Let $N$ be a positive integer. For every $d ∣ N$ such that $(d, N / d) = 1$ there exists an Atkin-Lehner involution $w_{d}$ of the modular curve $X_{0} (N)$ . Let $B (N)$ be the group of all…

math.NT2025

Tetragonal modular quotients $X_{0}^{*} (N)$

Petar Orlić

Let $N$ be a positive integer. For every $d ∣ N$ such that $(d, N / d) = 1$ there exists an Atkin-Lehner involution $w_{d}$ of the modular curve $X_{0} (N)$ . The curve $X_{0}^{*} (N)$ is a quot…

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

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

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

Tetragonal intermediate modular curves

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 $X_{Δ} (N)$ …

math.NT2024

Tetragonal modular quotients $X_{0}^{+ d} (N)$

Petar Orlić

Let $N$ be a positive integer. For every $d ∣ N$ such that $(d, N / d) = 1$ there exists an Atkin-Lehner involution $w_{d}$ of the modular curve $X_{0} (N)$ . In this paper we determine al…

math.NT2023

Tetragonal modular quotients $X_{0}^{+} (N)$

Petar Orlić

In this paper we determine all quotient curves $X_{0}^{+} (N)$ whose $Q$ or $C$ -gonality is equal to $4$ . As a consequence, we find several new cases when the modular…

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.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…

D-elliptic modular curves X0​(N)

Tetragonal modular quotients of X0​(N)

Tetragonal modular quotients X0∗​(N)

Morphisms on the modular curve X0​(p) and degree 6 points

Intermediate modular curves with infinitely many quartic points

Modular curves X0​(N) of density degree 5

Tetragonal intermediate modular curves

Tetragonal modular quotients X0+d​(N)

Tetragonal modular quotients X0+​(N)

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

Gonality of the modular curve X0​(N)

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

Tetragonal modular quotients of $X_{0} (N)$

Tetragonal modular quotients $X_{0}^{*} (N)$

Morphisms on the modular curve $X_{0} (p)$ and degree $6$ points

Modular curves $X_{0} (N)$ of density degree $5$

Tetragonal modular quotients $X_{0}^{+ d} (N)$

Tetragonal modular quotients $X_{0}^{+} (N)$

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

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