Quadratic degree recursion for elliptic multiplication ($\mathrm{deg}[n]=n^2$)

The degree parallelogram identity for endomorphisms of an elliptic curve gives $d_{n+1}+d_{n-1}=2d_n+2$ for $d_n=\mathrm{deg}[n]$, with $d_0=0$ and $d_1=1$. Induction gives $d_n=n^2$ in every characteristic. A zero pullback on differentials therefore does not mean that multiplication is the zero morphism.