So I was flying from Leeds to New York and stumbled across a pirate in an Eclipse bomber at a jumphole in Magellan. Of course he ran, but what was surprising was he led me to a hostile pirate base named Port Tortuga. It was right at the corner intersection of A8 and B7. You can see the output from the ship nav in the guncam pic below.
The base seems pretty well built up, but I imagine it could be crushed with the combined might of your navies.