I'm guessing that their 0.0 base of operations is the CVY-UC system in the Curse region based on the description of their history:
We decided to move into Curse finding it had good rats and lots of great targets. During our timezone we found a system nearly empty , dead end , great system to live in. However during the Euro timezone we found out that a major alliance lived there namely TCF.As well their kill board has the most kills in that system (354, over 250 more than the next highest) and my locator agent has put them there a few times. Looking at a map of Curse CVY-UC is definitely in TCF's area of influence and the best cul-de-sac system in the region.
I'm also confident that their low sec base in Derelik region is in Faspera system. Between these two points I hope to have some chances to see them and perhaps even engage an opprotunistic target although I would prefer to keep my fighting to Empire where neutrals could not interfere and bubbles would not be a concern but I will try to do what I have to in order to bring the fight to them. I know they love the Broadsword in FINEG (used in 424 kills, almost twice as much as the next highest which is the Ishtar at 232).
I'm currently guessing their time zone is west coast NA making it difficult for me to catch them in their prime time. On the other hand, perhaps that is better for me to avoid getting seriously outnumbered 3+ to 1. Make no mistake, I'm on my own here and its better if they are not working together when I move to engage.