There is a discontinuity in curvature where each arc meets. It’s possible to make joins between curves smoother using Euler spirals, but I don’t know how to use them well enough to apply them to eggs. https://en.m.wikipedia.org/wiki/Euler_spiral

I recently tried to draw f holes using Euler spirals, but they turned out too short and fat, and I gave up on them. But they are quite fun to draw on a computer by simple numerical integration, ignoring all the more complicated mathematics in the wikipedia article. Perhaps I could have made my f holes more elegant by understanding the parts I ignored… https://en.m.wikipedia.org/wiki/Sound_hole