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Nov 21, 2018 at 16:52 comment added abx I am not sure what you call a "Weil pairing on $G$", but if you mean the restriction of the Weil pairing (which is unique and canonical), the answer is obviously no: just take for $G$ a totally isotropic subspaces of $A[\ell]$.
Nov 21, 2018 at 16:38 history asked A. GM CC BY-SA 4.0