We should note that in Christian Scriptures, there were two men named Jesus, and both in trouble with the authorities. Not surprising, as Jesus/Yeshu'a/Joshua was a common Jewish name at that time.
One, Jesus Bar Abbas (Son of the Father) seems to have been a Zealot guerilla leader held by the Romans. The other, Jesus the Nazarene, was an itinerant Essene preacher who had caused a ruckus in theTemple because he disliked the profiteering of the money-changers there.
According to the myths, Pilate offered the people of Jerusalem the choice of which of these prisoners he would release to mark the Passover festival. There is a lot wrong with this. In the first place, Roman Procurators did not release important rebel leaders at the whim of the mob. Ever. In the second place, a brawl in the Temple precincts was a matter for the Temple Segens (bailiffs) to deal with, not the Roman garrison. Finally, the Temple money-changers were an essential service, but only to Jews. If you went into the Temple to make a sacifice, you had to buy your animal -a dove in most cases. Such a sacrifice could not be purchased with Roman denarii or sestertii, which bore the image of the Emperor in contravention of Jewish Law. So you had to exchange your Roman cash for Temple shekels at the money-changers. Naturally, the money-changers would make a profit on the deal and this is what Jesus of Nazareth objected to. None of this was of the slightest concern to the Romans, any more than theological disputes between Jewish sects were.
So we have one Jesus who the Romans were going to deal with, and another who was the responsibility of the Sanhedrin court. Jesus Barabbas, short of intervention by the Vestal Virgins -who were in Rome anyway - was going to be crucified, end of. To your left, through the door, one cross each.
Jesus of Nazareth? That's where things get speculative. For the public order offence, a fine and a lecture, probably. But the preaching? The anti-authoritarian attitude? The large number of converts? A problem for the heads of a theocratic state. But he had committed no blasphemy and had broken no religious laws; just preached a different way of applying them and predicted the end of the world. At a reasonable guess, I'd say they exiled him to Alexandria or somewhere where he could philosophise and preach till he was blue in the face without bothering them. Whereupon he went to ground until his friends could make arrangements, nipped back to have a last word with his followers, left his brother in charge and buggered off!
Paul, coming into the religion business years later, probably knew both stories, and conflated them in such a way as to make his new religion into the kind of mystery 'dying god' cult his Graeco-Roman target audience would recognise.