Beth Malmskog, Christopher Rasmussen
Published 2014-07-29, updated 2016-01-15Version 2
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.
Comments: 27 pages; A previous lemma was incorrect and has been removed; Corrected computation has identified 18 new such curves (63 in total)
Covering groups and their integral models
Integral Models of $X_0(N)$ and Their Degrees
A note on Picard curves of CM-type
![QR code for arXiv:1407.7892 [math.NT]](http://oss.arxitics.com/images/favicon.svg)