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We investigate the problem of describing a one-parametric family of elliptic functions which uniformizes a given family of ramified coverings of the Riemann sphere with maximal possible ramification over infinity. We find a PDE for the family of functions and use it to deduce a system of ODEs for their critical points.doi:10.15393/j3.art.2018.5290 fatcat:56nezkoexvhu5pv7qbqmwadqua