Important historical evidence comes from the pen of the Roman historian Tacitus (c. 56—120). He was a careful scholar, so his brief reference to the historical Jesus is very important. His collection of books called The Annals includes the famous story about the six-day fire, that burned much of Rome in July AD 64 and was set by Emperor Nero himself. To put that rumor to rest, Nero blamed Christians for setting the fire. Tacitus describes the support for the homeless provided by Nero and the rebuilding of the city. However, none of this did away with the suspicion that the fire had been started on Nero's orders:
Consequently, to get rid of the report, Nero fastened the guilt and inflicted the most exquisite punishments on a class hated for their disgraceful acts, called Chrestians by the populace. Christ, from whom the name had its origin, suffered the extreme penalty during the reign of Tiberius at the hands of one of our procurators, Pontius Pilatus, and a most mischievous superstition, thus checked for the moment, again broke out not only in Judaea, the first source of the evil, but even in Rome, where all things hideous and shameful from every part of the world find their centre and become popular. Accordingly, an arrest was first made of all who pleaded guilty; then, upon their information, an immense multitude was convicted, not so much of the crime of firing the city, as of hatred against mankind. Mockery of every sort was added to their deaths. Covered with the skins of beasts, they were torn by dogs and perished, or were nailed to crosses, or were doomed to the flames and burnt, to serve as a nightly illumination, when daylight had expired.
Tacitus then returns to the topic of Nero's reputation and the effect on it of these events:
Nero offered his gardens for the spectacle, and was exhibiting a show in the circus, while he mingled with the people in the dress of a charioteer or stood aloft on a car. Hence, even for criminals who deserved extreme and exemplary punishment, there arose a feeling of compassion; for it was not, as it seemed, for the public good, but to glut one man's cruelty, that they were being destroyed.
Tacitus misspelled Christian in the passage, but he reported that the error was a mistake of the crowd that he then corrected when he mentioned “Christ.” The fact that he calls Jesus,
"Christ" doesn't imply any belief that Jesus is the Messiah. It probably just reflects how Christians were referring to Jesus at that time. His reference that Jesus was executed doesn't refer specifically to crucifixion, but the fact that some Christians were crucified indicates that Nero was aware of the tradition.
Finally, Tacitus confirms the canonical gospel portrait that Pilate executed Jesus as an enemy of Rome. There is nothing mentioned about any Jewish involvement in the Crucifixion.