A note on Jacobians of quasiplatonic Riemann surfaces with complex multiplication (Q2039264)

A quasiplatonic Riemann surface is a pair \((X,G)\) where \(X\) is a Riemann surface of genus at least \(2\) and \(G\) is a group of automorphism such that \(X/G\) is a rational curve and the projection \(X \rightarrow X/G\) has only three critical values. In this short note the author considers an infinite series of quasiplatonic Riemann surfaces with associated group a semidirect group of the Klein group of order \(4\) by a cyclic group of order at least \(6\). Using a classification of these covers proved by himself in a preceding paper, he proves that the Jacobian variety of these curves admits complex multiplication. He moreover provides a criterium to prove similar results for more quasiplatonic Riemann surfaces.