A.T. Robertson Commentary Luke 4:31

"And he came down to Capernaum, a city of Galilee. And he was teaching them on the sabbath day:" — Luke 4:31 (ASV)

Came down (κατηλθεν). Mr 1:21 has the historical present,

they go into (εισπορευοντα). Capernaum (Tell Hum) is now the headquarters of the Galilean ministry, since Nazareth has rejected Jesus. Luke 4:31–37 is parallel with Mr 1:21-28 which he manifestly uses. It is the first of Christ's miracles which they give.

Was teaching them (ην διδασκων αυτους). Periphrastic imperfect. Mark has εδιδασκεν first and then εν διδασκων. "Them" here means the people present in the synagogue on the sabbath, construction according to sense as in Mr 1:22.