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In this note, I study a comparison map between a motivic and \'{e}talecohomology group of an elliptic curve over $\mathbb{Q}$ just outside the rangeof Voevodsky's isomorphism theorem. I show that the property of an appropriateversion of the map being an isomorphism is equivalent to certain arithmeticalproperties of the elliptic curve.

On the Arithmetic of Elliptic Curves and a Homotopy Limit Problem