The Constellation is a bit of a mystery ship. We know that the Constellation class USS Hathaway was launched as early as 2285 ("Peak Performance"), but we also know that the USS Constellation herself was in service as late as 2371 ("The Abandoned"). Given that we see so few of these ships, I've tried to suggest that they have had something of a troubled history - Picard described the Constellation class USS Stargazer as "underpowered", which led to most of the speculation here. I imagine that ships this old and rare wouldn't really be useful anymore beyond running supplies and suchlike.
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