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We provide new examples of curves of genus 6 or 10 attaining the Serre bound.They all belong to the family of sextics introduced in [19] as a ageneralization of the Wiman sextics [36] and Edge sextics [9]. Our approach isbased on a theorem by Kani and Rosen which allows, under certain assumptions,to fully decompose the Jacobian of the curve. With our investigation we areable to update several entries in \url{http://www.manypoints.org} ([35]).

New sextics of genus 6 and 10 attaining the Serre bound