Star Trek Deckplan Federation

The J-class originally appeared in Star Trek's first season episode Mudd's Women, where it was seen on screen as an indistinct blob of light. In Star Trek Remastered, it was replaced by an all-new CGI ship, a tubular hull with a pair of warp nacelles.

In the episode, Harcourt Fenton Mudd had stolen the ship from Captain Leo Walsh, whose identity he also used. He was using it to transport three women whom he had "treated" with the legendary "Venus Drug." As his ship was about to explode, he and the women were beamed away by the USS Enterprise

The ship was also used (with the addition of portholes) as the Aurora in The Way to Eden. I used that version to deduce the size, some 38.85 metres long.