My wife found this web page testing several different ways of hard boiling an egg:
hard boil an egg.
I don't plan to change my current technique as a result of reading it, though. I do them on an induction cooker, turning off the heat when it gets to a full rolling boil, which takes under 10 minutes, and letting them sit in that for 19 minutes. I put some baking soda in the water, I think it helps make them easier to peel, although using 'old' eggs is probably the best method in general, since some of the liquid evaporates, leaving more of an air bubble inside.
I tried the shaking method once to get them to peel easily, the eggs fell apart. Maybe I shook them too hard?