Rational points on hyperelliptic Atkin-Lehner quotients of modular curves and their coverings

verfasst von

Nikola Adzaga, Shiva Chidambaram, Timo Keller, Oana Padurariu

Abstract

We complete the computation of all Q-rational points on all the 64 maximal Atkin-Lehner quotients X(N)

^∗ such that the quotient is hyperelliptic. To achieve this, we use a combination of various methods, namely the classical Chabauty–Coleman, elliptic curve Chabauty, quadratic Chabauty, and the bielliptic quadratic Chabauty method (from a forthcoming preprint of the fourth-named author) combined with the Mordell-Weil sieve. Additionally, for square-free levels N, we classify all Q-rational points as cusps, CM points (including their CM field and j-invariants) and exceptional ones. We further indicate how to use this to compute the Q-rational points on all of their modular coverings.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Externe Organisation(en)

University of Zagreb
Massachusetts Institute of Technology (MIT)
Universität Bayreuth
Boston University (BU)

Typ

Artikel

Journal

Research in Number Theory

Band

8

Publikationsdatum

12.10.2022

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Algebra und Zahlentheorie

Elektronische Version(en)

https://doi.org/10.1007/s40993-022-00388-9 (Zugang: Offen)