What ended Roman persecution of the Christians?

There is no real evidence of the Romans persecuting Christians before at least 97 CE, and only sporadic periods of persecution even after that. Professor Keith Hopkins (A world full of gods: the Strange Triumph of Christianity) says that although in its early years Christianity was both illegal and at loggerheads with the state, it was largely ignored until the three purges of 250, 257 and 303- 311.

Persecution of the Christians ended early in the fourth century, because Christianity received state patronage under Emperor Constantine.