Luke 4:16
And he came to Nazareth, where he had been brought up:
nd, as his custom was, he went into the synagogue on the sabbath day,
and stood up for to read.

Luke 4:31
And came down to Capernaum, a city of Galilee,
and taught them on the sabbath days.


From Har Nitai or Arbel you can see down to Capernaum. And it really is .. DOWN.

I'll see if I can find a picture.
Here is one (and tap on it with the mouse to enlarge.)
http://www.bibleplaces.com/wp-content/uploads/2015/08/1.4-Jezreel-Valley.jpg

From modern Nazareth you would take a long road through Galilee. This language does not fit.

On that map it is across the hilly area to "Cana?", then down to the Turan Valley, then back up and across the Galilee hills, taking the valley route between Nitai (not on map) and Arbel, which is the Khirbet Wadi Hamam (synagogue unearthed there) then finally through to the Kinneret and up to Capernaum. There is no way that "down to Capernaum" is sensible writing.

Conzelmann points this out in The Theology of St. Luke (1954 German, English 1961).
Here is the report from Karel Hanhart.

Studies in John (1970)
Karel Hanhart
https://books.google.com/books?id=ZnweAAAAIAAJ&pg=PA31

"the going 'down' to Capernaum, while Nazareth does not stand on a hill (p. 39)"

This is actually showing both that Nazareth is not on the brow of a hill, and that down to Capernaum does not fit.

Steven