Degtyarev, Alex2022-02-172022-02-172021-11-290027-7630http://hdl.handle.net/11693/77466We prove that the maximal number of conics in a smooth sextic K3-surface X ⊂ P4 is 285, whereas the maximal number of real conics in a real sextic is 261. In both extremal configurations, all conics are irreducible.EnglishArticle10.1017/nmj.2021.32152-6842