I'm looking for as many examples/applications as possible of the use of embedding a smooth projective geometrically connected curve $X$ over a number field $k$ with $X(k)\neq \emptyset$ into its Jacobian (via a rational point). Please do not take the meaning of "use" to seriously.
I know of
Chabauty's method of proving a special case of the Mordell conjecture.
Faltings' use of the Torelli map in his proof of the Shafarevich conjecture for curves.
Raynaud's theorem (previously Manin-Mumford conjecture).
The Bogomologov conjecture (proven by Ullmo and Zhang).
The Mordell-Lang theorem.
In some of these examples the embedding of X into its Jacobian is simply part of the statement. I also consider this as "useful".
Are there any other nice examples? They don't have to be as difficult as the ones mentioned above.