where is shuttle to coruscant from tython in SWTOR?

Answer 1

There is no shuttle to Coruscant from Tython.  The shuttle from Tython can take you 1)  to the Republic Fleet (where you can get a shuttle to Coruscant, either directly there or by means of the Esseles Flashpoint mission), or 2) if you have a ship of your own, it can take you directly to your ship.