How do I filter the "admin/content" page through it's url?
By default this is not possible.
Easiest I can see would be to create a view - if you have views module installed - that has the same path which will override the default Drupal content screen.

Then you can either create argument for the content type as part of url and/or expose filters and since the filters are being passed via get parameter, you will be able to construct an url to point to the filter selection.

Which is almost what administration views module does. You might want to extend these views with arguments, filters, etc...

Other option would be to create custom functionality that would "hook" into the default functionality.