1. A computer system, comprising: a configuration comprising one or more cores configurable between a single thread (ST) mode and a multithreading (MT) mode, wherein the ST mode addresses a primary thread and the MT mode addresses the primary thread and one or more secondary threads on shared resources of each of the one or more cores; and a multithreading facility configured to control utilization of the configuration to perform a method comprising: executing, by a core, a retrieve multithreading capability information (RMTCI) instruction, wherein the execution comprises: obtaining thread identification information that identifies a multithreading capability of the configuration; storing the obtained thread identification information; and determining whether the configuration previously had MT enabled based on the obtained thread identification information.