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.Comment: 27 pages; A previous lemma was incorrect and has been removed;
Corrected computation has identified 18 new such curves (63 in total