I have a first edition of Brodie’s book. But I thought it best to post the most conservative list since the poor uneducated in Smithism mormons are already in shock when they learn that there are so many and that many of the women were still married to living men and that many of the women have sworn to the fact that their relationship with Joe was sexual, albeit usually brief.
You probably know Fawn Brodie had extraordinary access to secret Mormon archives through her family connections -- her uncle was LDS President David McKay and her father was the President of BYU. She was careful not to use any information in her histories that was not in the public domain. But she also said on many occasions that her tally of 56 vastly understated the number of Joseph's conquests.
Also, as you probably know, Joseph's most effective approach was to ask a young lady if she wanted to spend eternity in heaven or hell. The outcome depended on the degree to which the woman pleased her prophet.