"东罗马帝国的" can be translated as "Byzantine" or "of the Byzantine Empire" in English.
"Byzantine" is often used as an adjective to describe things related to the Eastern Roman Empire (Byzantine Empire), such as "Byzantine art"（东罗马/拜占庭艺术）, "Byzantine architecture"（东罗马/拜占庭建筑）.
When you want to explicitly express the ownership or association with the Byzantine Empire in a more detailed context, you can use "of the Byzantine Empire", for example, "the history of the Byzantine Empire"（东罗马帝国的历史）.