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.