Computing quadratic points on modular curves 𝑋₀(𝑁)

DOI10.1090/MCOM/3902arXiv2303.12566MaRDI QIDQ6203468

Author name not available (Why is that?)

Publication date: 28 February 2024

Published in: (Search for Journal in Brave)

Abstract: 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 $X_0(N)$ of genus up to $8$, and genus up to $10$ with $N$ prime, for which they were previously unknown. The values of $N$ we consider are contained in the set [ mathcal{L}={58, 68, 74, 76, 80, 85, 97, 98, 100, 103, 107, 109, 113, 121, 127 }.] We obtain that all the non-cuspidal quadratic points on $X_0(N)$ for $NinmathcalL$ are CM points, except for one pair of Galois conjugate points on $X_0(103)$ defined over $mathbbQ(sqrt2885)$. We also compute the $j$-invariants of the elliptic curves parametrised by these points, and for the CM points determine their geometric endomorphism rings.

Full work available at URL: https://arxiv.org/abs/2303.12566

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Computing quadratic points on modular curves 𝑋₀(𝑁)

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6203468)