What efficient algorithms are there to compute the $S$-units of a given imaginary quadratic field $K$, where $S$ is a finite set of non-archimedean primes?
Computing $S$-units are implemented in computer algebra software like Sage and Pari. But they are implemented only in general for number fields (as far as I know), I would like to use an algorithm specialized for imaginary quadratic fields in case it could improve efficiency.
Please let me know if such an algorithm is implemented somewhere or if such an algorithm is known to exist.