The current official git mirror of the Firefox code base (also known as "gecko" or "mozilla-central") can be found at https://github.com/mozilla/gecko-dev. This repository contains all of the branches that are part of mainline development, including the train branches mozilla-central (nightly), mozilla-aurora (developer edition), mozilla-beta, and mozilla-release.
If you are looking to work with other Mozilla branches, https://github.com/mozilla/gecko-projects might also be of use. This repository contains the project branches (also known as "twigs") whose use varied.
If you would prefer to use git directly with the hg repositories this workflow is describes how to proceed. Using this approach will also let you push directly from your git repository to mercurial.