Degtyarev, AlexRams, Slawomir2025-02-192025-02-192024-10-060179-5376https://hdl.handle.net/11693/116403We prove the sharp upper bound of at most 52 lines on a complex K3-surface of degree 4 with a non-empty singular locus. We also classify the configurations of more than 48 lines on smooth complex quartics.EnglishCC BY 4.0 (Attribution 4.0 International Deed)https://creativecommons.org/licenses/by/4.0/K3-surfaceQuarticElliptic pencilIntegral latticeDiscriminant formArticle10.1007/s00454-024-00690-61432-0444