Certainly Caiaphas, the High Priest, was behind it all. Ananus deferred to what his son-in-law wanted.
Pilate was cornered into crucifying Jesus because Caiaphas knew a public stoning would backfire- if he could even find enough Jews to throw stones at Jesus. Jesus had to be railroaded and Pilate probably owed Caiaphas a favor. The Temple probably paid Pilate personally a huge amount of money every year as a bribe.
But there is much more to the story. If you read Josephus. In Hagan’s “Passover” and “Fires of Rome” it is laid out.
Jesus was executed early in the Passover because the Syrian President and the second most powerful man in the Roman Empire at the time, Lucius Vitellius, was coming to Jerusalem for the celebration, on a special assignment from Tiberius. The event had to be peaceful or Rome might pull their backing of the High Priesthood as de facto rulers of Judea.
The year would have been AD 36.
Hagan also goes into how that year is derived. A lot has to do with the arrest and execution of John the Baptist, and Herod Antipas’ attempted invasion of Nabotea, which was rebuffed with great losses.