On Rational Points of Algebraic Curves of Genus One Original Research Article

Tate proved a theorem on rational points of torsors ("Torsors" means "Homogeneous spaces," in sequel we use "torsors" in this meaning) of T / K, where K is a local field, T is a Tate curve. In this paper we extend the above theorem to the case where T is a twist of a Tate curve, and apply our results to the global case.