Why did the Romans rename Jersusalem "Aelia Capitolina" in 135 AD?

Image:  Jerusalem depicted in the sixth century Madaba mosaic map, on the floor of a Byzantine church in Madaba, Jordan.

One of the great things about teaching an introductory New Testament course to undergraduates semester after semester is getting the questions to which you do not know the answer.

This semester I was doing my standard lecture on Greco-Roman and Jewish backgrounds to the NT, including making mention of the disastrous Second Jewish War against Rome (132-135 AD) which ended with the Romans leveling Jerusalem a second time (after its total destruction in 70 AD), renaming it Aelia Capitolina, building a temple to Jupiter on the temple ruins, and forbidding Jews to enter the city.  This event obviously had huge ramifications for early Jews and Christians as it further contributed to their dispersion from Palestine.  A student asked:  "Why was Jerusalem re-named Aelia Capitolina?"  I had to tell him I did not know the answer, but on the class break I googled it and found this answer on the online Encyclopedia Brittanica:

Aelia Capitolina,  city founded in ad 135 by the Romans on the ruins of Jerusalem, which their forces, under Titus, had destroyed in ad 70. The name was given, after the Second Jewish Revolt (132–135), in honour of the emperor Hadrian (whose nomen, or clan name, was Aelius) as well as the deities of the Capitoline Triad (Jupiter, Juno, and Minerva). A sanctuary to Jupiter was built on the Temple Mount, and statues of Roman deities were erected in the city, in intentional violation of Old Testament law. The area was walled and a large foreign population imported; Jews were generally forbidden entrance to the city. The present walls of the Old City of Jerusalem follow the layout of the Roman walls. The name was used until Christianity became the official religion of the Roman Empire in the 4th century.

So, I now have an answer to the question.

JTR