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Publikationsdetails

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)