How did Christianity enter Rome?

"Paul addressed the book we call Romans to Christians living in Rome. At the time the letter was written, he had not yet visited the city as far as we know and he does not personally know Christians in Rome. Although he may have something about the church through Aquila and Priscilla (Acts 18:1-4), there is nothing to suggest he ministered there until he arrives about A.D. 60 (Acts 28:11-31). How did Christianity come to Rome?

 According to Eusebius, Peter followed the ach-heretic Simon the Sorcerer (Acts 8) to Rome in the second year of Claudius (A.D. 42). According to Eusebius, the Gospel Peter preached at this time was so well received the Roman people demanded a written copy, which became the Gospel of Mark, a tradition also found in Irenaeus.

Eusebuis, Hist. eccl. 2.15.1 And so greatly did the splendor of piety illumine the minds of Peter’s hearers that they were not satisfied with hearing once only, and were not content with the unwritten teaching of the divine Gospel, but with all sorts of entreaties they besought Mark, a follower of Peter, and the one whose Gospel is extant, that he would leave them a written monument of the doctrine which had been orally communicated to them.
Irenaeus, Haer. 3.1 Matthew also issued a written Gospel among the Hebrews in their own dialect, while Peter and Paul were preaching at Rome, and laying the foundations of the Church.

..... consensus view is that the church was founded by believers who returned to Rome after Pentecost. Jews had contact with Rome as early as 160 B.C. Pompey brought Jews captured at Jerusalem to Rome in 63 B.C. (Anitq. 14.4.5) and by the time Romans was written the Jewish population in Rome may have been as high as 50,000. Fitzmyer also argues for at least thirteen synagogues based on inscriptional evidence. In addition to these inscriptions there are thousands of funerary inscriptions in the catacombs.

There is evidence of Christians in Rome as early as A.D. 49, when Claudius expelled Jews for rioting over “Chrestus,” likely a Latinized form of Christos, the Greek translation of Messiah. Luke refers to this decree in Acts 18:2-4. Soon after arriving in Corinth, Paul meets Aquila and Priscilla, Jewish tentmakers forced to leave Rome by Claudius." ReadingActs

And the night following the Lord stood by him, and said,

Be of good cheer, Paul: for as thou hast testified of me in Jerusalem,

so must thou bear witness also at Rome.

Acts 23:11