The various Shiʿa movements that have sprung up over the centuries trace their origins, obviously, to Ali ibn Abi Talib, the cousin and son in-law of Muhammad. But apart from that common origin there have (again, obviously) been a number of disagreements within the Shiʿa community over which line of descent from Ali was legitimate. These points of divergence can happen at any point along the family tree. For example, two of the tree largest extant Shiʿa branches, the Twelvers and the Ismaʿilis, shared the first several imams but splintered over the question of who succeeded Jafar al-Sadiq (d. 765). But through those shared early imams they both trace their lineages back to Ali through his second son (by Muhammad’s daughter Fatimah), Husayn.
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