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

Autori
Adžaga, Nikola ; Chidambaram, Shiva ; Keller, Timo ; Padurariu, Oana

Izvornik
Research in number theory (2522-0160) 8 (2022); 87, 24

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Rational points ; Curves of arbitrary genus or genus 6= 1 over global fields ; arithmetic aspects of modular and Shimura varieties

Sažetak
We complete the computation of all Q-rational points on all the 64 maximal Atkin-Lehner quotients X0(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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Napomena
Rad je prihvaćen na Algorithmic Number Theory
Symposium, ANTS-XV, konferenciji koja se održala u
kolovozu 2022. Svi radovi s konferencije (njih 26)
objavljeni su u posebnom broju časopisa Research
in Number Theory.

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