What is the name of the Eastern Christian empire centered on Constantinople?

The story behind the answer

This Eastern Christian empire was the Greek-speaking continuation of the Roman Empire, ruled from Constantinople for over a millennium and grounded in Orthodox Christianity. Its rulers saw themselves as Roman emperors, and the city was the political, religious, and economic hub of their world.

It codified Roman law under Justinian (the Corpus Juris Civilis), raised architectural marvels like Hagia Sophia, and preserved classical learning while serving as a bulwark between Europe and the Islamic world. Don’t confuse it with the Ottoman Empire (Muslim, later conquerors of Constantinople), the Holy Roman Empire (Central European, Latin Christian, centered far to the west), or the short-lived Latin Empire (a Crusader state that occupied Constantinople 1204–1261).