• Media type: Text; E-Article
  • Title: Rational points on hyperelliptic Atkin-Lehner quotients of modular curves and their coverings
  • Contributor: Adžaga, Nikola [Author]; Chidambaram, Shiva [Author]; Keller, Timo [Author]; Padurariu, Oana [Author]
  • Published: Heidelberg : Springer, 2022
  • Published in: Research in number theory : a SpringerOpen journal 8 (2022), Nr. 4 ; Research in number theory : a SpringerOpen journal
  • Issue: published Version
  • Language: English
  • DOI: https://doi.org/10.15488/13731; https://doi.org/10.1007/s40993-022-00388-9
  • ISSN: 2522-0160
  • Keywords: quadratic Chabauty ; descent ; conjecture
  • Origination:
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  • Description: 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.
  • Access State: Open Access