dear, I need a precise reference to the fact that the connected component of $ Pic (A) $, where $ A $ is an abelian variety over a field $ k $ consists of the following set $\{L \in Pic (A) : T ^*_x L \cong L \ \textrm{for all} \ x \in X \} $ where $ Tx $ is the translation by $ x $

In the books of abelian varieties and the Mumford Milne not have that.