# Weil matches in abelian varieties restricted to subgroups of a given order

Leave $$A$$ be an abelian variety of dimension $$g$$ defined on a numeric field $$K$$. Suppose $$A$$ It has a main polarization and $$ell$$ It's a prime number. We have a pair of Weil:

$$e_ ell: A[ell] times A[ell] rightarrow mu_ ell$$

I do not know if Weil's pairing is unique, so my question is this:
Given a subgroup $$G subset A[ell]$$ of order $$ell ^ 2$$, there's a couple from Weil $$e_ ell$$ (possibly depending on $$G$$) such that there are $$P, Q in G$$ Y $$e_ ell (P, Q)$$ It is a primitive $$ell$$-the root of the unit?

I know by here that for any point. $$P in G$$, there is a point $$Q in A[ell]$$ such that $$e_ ell (P, Q)$$ It is a primitive $$ell$$-the root of the unit. Thanks in advance for the comments and answers.