Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 18 / 4 / ii / Solution

Pull $L$ back by the morphism of varietiesThe fiber of this line bundle over $x$ is ${\phi }^{\ast }{T}_x^{\ast }L$. An abelian variety is connected, so the preceding constancy of line bundle degree in a family applies. Consequently $\boxed{\mathrm{deg}({\phi }^{\ast }{T}_x^{\ast }L)=\mathrm{deg}({\phi }^{\ast }L)}$ for every $x\in X$.