Let $(X, L)$ and $(Y, M)$ be two polarized abelian varieties .
According to Birkenhake C. and Lange H. in Complex Abelian Varieties a homomorphism of polarized abelian varieties $f:(Y, M)\longrightarrow (X, L)$ is a homomorphism of complex tori $f:Y\longrightarrow X$ such that $f^{*}c_1(L) = c_1(M)$.
Question: It's true that $f^*c_1(L)=c_1(f^*L)$?