Picard curves over Q with good reduction away from 3
Number Theory
2019-02-20 v2
Abstract
Inspired by methods of N. P. Smart, we describe an algorithm to determine all Picard curves over Q with good reduction away from 3, up to Q-isomorphism. A correspondence between the isomorphism classes of such curves and certain quintic binary forms possessing a rational linear factor is established. An exhaustive list of integral models is determined, and an application to a question of Ihara is discussed.
Keywords
Cite
@article{arxiv.1407.7892,
title = {Picard curves over Q with good reduction away from 3},
author = {Beth Malmskog and Christopher Rasmussen},
journal= {arXiv preprint arXiv:1407.7892},
year = {2019}
}
Comments
27 pages; A previous lemma was incorrect and has been removed; Corrected computation has identified 18 new such curves (63 in total)