A simple proof of a theorem of Parish
The aim of this short note is to give a new proof of a result of \textit{J. L. Parish} [J. Number Theory 33, 257-265 (1989; Zbl 0703.14023)] that, in an elliptic curve \(E\) defined over a number field \(K\) with complex multiplication over \(\bar{K}\), a torsion point which is rational over \(K(j(E))\) has order \(1,2,3,4,6\) (here \(j(E)\) is the \(j\)-invariant of \(E\)). The proof uses elementary class field theory.
scientific article; zbMATH DE number 1443392