Consequently, to get rid of the report, Nero fastened the guilt and inflicted the most exquisite tortures on a class hated for their abominations, called Christians by the populace. Christus, 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 the evil, but even in Rome, where all things hideous and shameful from every part of the world find their center and become popular.According to this Wikipedia page there is some pushback (because of course) but it seems pretty clear that this matches up with the story from the Gospel. An official named Pontius Pilate condemned Christ to crucifixion, 'the extreme penalty'. The pushback suggests that this note was added later by monks but the tone of the passage makes that hard to believe. It's also said that Tacitus could simply be repeating the beliefs of the Christians but he had access to official records and used them throughout his writings. There is no more reason to doubt him here then there is to doubt most of his writing.
Nero (about whom I'll write more) was a real piece of work. The above passage wasn't kidding when it said that he inflicted exquisite tortures on Christians. Tacitus describes some of their deaths:
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. 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.I've never heard of people being burnt to serve as torches. That's pretty awful. I'm surprised that Nero doesn't get more notoriety in Christian circles.