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It was a treaty between England and the U.S.

Reid v. Covert is not just a case. It is THE landmark case on the supremecy of the Constitution over treaties.

Here is what the Court wrote: (my bold)

P.17 - There is nothing new or unique about what we say here. This Court has regularly and uniformly recognized the supremacy of the Constitution over a treaty.*fn33 For example, in Geofroy v. Riggs, 133 U.S. 258, 267, it declared:

P.18 - This Court has also repeatedly taken the position that an Act of Congress, which must comply with the Constitution, is on a full parity with a treaty, and that when a statute which is subsequent in time is inconsistent with a treaty, the statute to the extent of conflict renders the treaty null.*fn34 It would be completely anomalous to say that a treaty need not comply with the Constitution when such an agreement can be overridden by a statute that must conform to that instrument.