Oh dear. Tiberius was the emperor at the time Christus’ execution. He was the first emperor to mention him. 7 years after the execution, one of Tiberius governors writes to him and asks if Rome has an official position on these followers of Christus because they are starting to make trouble in his district. Tiberius writes back that no Rome doesn’t have an official position on it. But yeah Pilate’s execution of this dude is causing problems and they’ve reached Rome too. Do what you need to to keep the peace.
Only Tiberius letter survives, the rest is contextual.
History over Randy quaid ramblings, my dear.