AK3K3surfaceXXdefined over a fieldkkof characteristic00is calledsingularif the Néron-Severi latticeNS(X)\mathrm {NS}(X)ofX⊗k¯X\otimes \overline {k}is of rank2020. LetXXbe a singularK3K3surface defined over a number fieldFF. For each embeddingσ:F↪C\sigma : F\hookrightarrow \mathbb {C}, we denote byT(Xσ)T(X^\sigma )the transcendental lattice of the complexK3K3surfaceXσX^\sigmaobtained fromXXbyσ\sigma. For each primep\mathfrak {p}ofFFat whichXXhas a supersingular reductionXpX_{\mathfrak {p}}, we defineL(X,p)L(X, \mathfrak {p})to be the orthogonal complement ofNS(X)\mathrm {NS}(X)inNS(Xp)\mathrm {NS}(X_{\mathfrak {p}}). We investigate the relation between these latticesT(Xσ)T(X^ \sigma )andL(X,p)L(X,\mathfrak {p}). As an application, we give a lower bound for the degree of a number field over which a singularK3K3surface with a given transcendental lattice can be defined.