https://www.etymonline.com/word/emperor

The Roman emperors took the title of "Imperator" meaning something like "conquering general" because the Romans might have revolted if the rulers took the title of "Rex" (King).

The concept of "Empire" is a later invention that the people of that time would not have used.

https://www.etymonline.com/word/empire

The etymology is literally 'an area which is ruled', which Pilate's central role seems to establish.

So, I think you are playing a word game rather than thinking clearly.

Moreover, if you understand how the Roman governorship worked you see clearly that the Romans could never have crucified Christ. Once Pilate declares him innocent it would be murder to crucify him anyway.