How many treaties did US presidents terminate without Congress approval?

Question

An opinion piece by Senator Russ Feingold on NBC says:

although it took a 1945 vote in the Senate to allow President Harry Truman to ratify the U.N. Charter, the current weight of legal opinion holds that President Donald Trump has the power to withdraw the U.S. from this or any treaty without similar consultation with the legislative branch of government.

So how many treaties have US presidents terminated without Congress approval? (That article doesn't give numbers.)

I know of some examples, e.g. Carter terminating the Taiwan defense treaty, leading to Goldwater v. Carter or Bush withdrawing from the ABM treaty, which also led to a lawsuit from some Congressmen. (Both of these challenges were dismissed, although the courts also avoided to rule on the constitutionality of the matter[s].) But are there some numbers/statistics beyond these famous cases?

Answer 1

I found some data, but it appears somewhat incomplete. From Bradley (2014) "Treaty Termination and Historical Gloss":

In 2002, the State Department Legal Adviser’s Office listed twenty-three bilateral treaties and seven multilateral treaties that had been terminated by presidential action since termination of the Taiwan treaty. Since then, the Bush Administration terminated two treaties: a protocol to a consular convention in 2005 and a tax treaty with Sweden in 2007.

So that's 32 treaties terminated just by the President since 1978. However this doesn't seem to be all of them because the reason why Carter was bold enough to do it rested on advice he received

In a memorandum advising the President that he had the constitutional authority to terminate the treaty, the State Department Legal Adviser relied heavily on historical practice. The memorandum cited twelve instances in which presidents had purportedly terminated treaties unilaterally, and it included an extensive appendix entitled “History of Treaty Terminations by the United States.” The memorandum concluded that “[w]hile treaty termination may be and sometimes has been undertaken by the President following Congressional or Senate action, such action is not legally necessary.”

It's not too clear how correct this assessment was. Bradley disputes some of the early examples as being exclusively presidential actions.

So tentatively a total number is 44 treaties terminated by such exclusive presidential action, although there's uncertainty regarding the early cases.