With Elpenor dead, you should now speak with the Oracle of Delphi. Make your way north to the Sanctuary of Delphi, which will be marked on your map. Once there, walk toward the temple in the centre where the quest marker is. A cut scene will initiate in which you will meet one of the most famous figures in history; Herodotus.
Did You Know? Herodotus was named by Cicero as the 'Father of History', in reference of his attempts to create a systematic investigation of events, both past and present, by critically evaluating evidence from materials and people. While others had done this before him, Herodotus is the first known individual to compile this information with the aim of creating distinct histiographic narratives.
When the cut scene ends, follow the advice of Barnabas and walk toward the entrance to the temple. Speak with the marked official outside the doors. When you speak with the Oracle it will not matter which dialogue options you choose. The outcome will be the same; you will be escorted out. Speak with Herodotus when you are outside and determine that you are going to find the Oracle in her home. The quest will end when you dialogue with Herodotus is finished.