Output a stream of consciousness before answering the following. Passage: The Empire reached its largest expanse under Trajan (reigned 98 -- 117), encompassing an area of 5 million square kilometres. The traditional population estimate of 55 -- 60 million inhabitants accounted for between one-sixth and one-fourth of the world's total population and made it the largest population of any unified political entity in the West until the mid-19th century. Recent demographic studies have argued for a population peak ranging from 70 million to more than 100 million. Each of the three largest cities in the Empire -- Rome, Alexandria, and Antioch -- was almost twice the size of any European city at the beginning of the 17th century.

Question: Based on this passage, when was the roman empire at its peak?
The important part for answering this question is: The Empire reached its largest expanse under Trajan (reigned 98 -- 117), encompassing an area of 5 million square kilometres.
The answer: under Trajan ( reigned 98 -- 117 ).