Computing Quadratic Points on Modular Curves X0(N)
- authored by
- Nikola Adžaga, Timo Keller, Philippe Michaud-Jacobs, Filip Najman, Ekin Ozman, Borna Vukorepa
- 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 X0(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 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 X0(N) for N ∈ L are complex multiplication (CM) points, except for one pair of Galois conjugate points on X0(103) defined over Q(√2885). We also compute the j-invariants of the elliptic curves parametrised by these points, and for the CM points determine their geometric endomorphism rings.
- Organisation(s)
-
Institute of Algebra, Number Theory and Discrete Mathematics
- External Organisation(s)
-
University of Zagreb
University of Warwick
Bogazici University
- Type
- Article
- Journal
- Mathematics of Computation
- Volume
- 93
- Pages
- 1371-1397
- No. of pages
- 27
- ISSN
- 0025-5718
- Publication date
- 05.2024
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Algebra and Number Theory, Computational Mathematics, Applied Mathematics
- Electronic version(s)
-
https://doi.org/10.48550/arXiv.2303.12566 (Access:
Open)
https://doi.org/10.1090/mcom/3902 (Access: Closed)
