Have you clicked the “File” menu within the notebook? There is a “File → Download” option that allows you to choose lots of download formats, including “TeX”. I have not tried downloading a notebook as LaTeX, but I use the “as notebook (ipynb)” option. On some browsers you may find that the file downloads with the extension “.json”. The notebooks are JSON files, but you would need to rename it to the extension “.ipynb” if you ever want to upload the file and use it again.
If you are planning to save copies of your work as a “backup” in case Coursera ever deletes your work (not a bad idea), you probably should use the “as notebook” option. If you download it as PDF or LaTeX, I think that would probably only be useful for printing.
You can also download and save all the files associated with the notebook by using the instructions here.