He ends up going to see Hanneman to ask about curriculum, and finds out he has a Crest.

"I unfortunately need to go elsewhere at the moment," Byleth told the group, turning.

"Oh, where to?" Caspar asked.

"Given that this position was given to me out of the blue, I'm going to need to ask for advice from the other teachers," he explained simply, before walking off. He was confident he could teach combat skills well enough, but academic stuff? Yeah, he was going to need some help planning that curriculum.

He decided to ask Hanneman first, despite Sothis protesting, 'What, not going to see Manuela? You could pretty easily get a good time with her, I'm sure!'

'Probably. And exactly why. This is too important to let myself get distracted,' Byleth mentally replied, making Sothis huff, but not argue further.

Hanneman was of course, happy to help, and gave Byleth a list of books he could familiarize himself with to teach the students with. "Thomas will be able to help you find these in the library, and any other subject matter you may have an interest in!" he assured Byleth. "By the way, do you know whether or not you have a Crest?"

When Byleth denied any knowledge, and admitted unfamiliarity with Crests, Hanneman was rather taken aback, then got excited at the prospect of telling Byleth about them. Though Byleth had to cut him off when he asked if his calendar was clear. If it would take days to tell him everything, then he was just going to ask for the basics.

"Right, good point, neither of us have the time for that," Hanneman deflated, before explaining that Crests were passed through the blood, though not always, and sometimes were dormant, only to reemerge in later descendants. After taking a sample of blood from Byleth, and running it through a few of his instruments, a sigil appeared. One that Hanneman was completely unfamiliar with, and gushed at the idea of finding an undiscovered Crest.

Byleth left, leaving Hanneman to ramble about what certain lines could mean, it was all going over his head anyway.