Joan-C. Lario, Anna Somoza
Published 2016-11-08Version 1
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.
Chabauty-Coleman computations on rank 1 Picard curves
Picard curves over Q with good reduction away from 3
Even icosahedral Galois representations of prime conductor
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