docker run -it alpine:latest sh -c "apk list -I | wc -l"

Returns 15 as of right now, so that's what it ships with by default (for their images at least). I tried `apk list -I -q | apk del -r -f` just for fun to remove them, but doesn't seem like it's possible, so 15 might be the least amount of packages possible, unless you build your own dist from alpine.