A note on Picard curves of CM-type

We extend the list of Picard curves of CM-type given by Koike and Weng. In particular, our list includes defining equations for the complete list of Picard curves of CM-type defined over $mathbb{Q}$ up to isomorphism. To this end, we improve their algorithm in some aspects: one needs to precise a root of unity in an accurate application of a Thomae-like formula well-suited for the Picard case, and also use an optimized strategy to evaluate the Riemann theta-series involved.