Quadratic Chabauty for Atkin–Lehner quotients of
modular curves of prime level and genus 4, 5, 6
Nikola Adžaga, Vishal Arul, Lea Beneish, Mingjie Chen, Shiva Chidambaram, Timo Keller, Boya Wen
Acta Arithmetica 208 (2023), 15-49
MSC: Primary 14G05; Secondary 11G30, 11G18.
DOI: 10.4064/aa220110-7-3
Opublikowany online: 5 June 2023
Streszczenie
We use the method of quadratic Chabauty on the quotients $X_0^+(N)$ of modular curves $X_0(N)$ by their Fricke involutions to provably compute all the rational points of these curves for prime levels $N$ of genus 4, 5, and 6. We find that the only such curves with exceptional rational points are of levels $137$ and $311$. In particular there are no exceptional rational points on those curves of genus 5 and 6. More precisely, we determine the rational points on the curves $X_0^+(N)$ for $N=137,173,199,251,311,157,181,227,263,163,197, 211,223,269,271,359$}.
Autorzy
- Nikola AdžagaDepartment of Mathematics
Faculty of Civil Engineering
University of Zagreb
10000 Zagreb, Croatia
e-mail
- Vishal ArulDepartment of Mathematics
University College London
London WC1E 6BT, United Kingdom
e-mail
- Lea BeneishDepartment of Mathematics
University of California at Berkeley
Berkeley, CA 94720, USA
e-mail
- Mingjie ChenSchool of Computer Science
University of Birmingham
Birmingham B15 2TT, United Kingdom
e-mail
- Shiva ChidambaramDepartment of Mathematics
Massachusetts Institute of Technology
Cambridge, MA 02139-4307, USA
e-mail
- Timo KellerIAZD, Leibniz Universität Hannover
30159 Hannover, Germany
and
Department of Mathematics
Universität Bayreuth
95440 Bayreuth, Germany
e-mail
- Boya WenDepartment of Mathematics
University of Wisconsin at Madison
Madison, WI 53706, USA
and
Simons Laufer Mathematical Sciences
Institute (formerly MSRI)
Berkeley, CA 94720-5070, USA
e-mail