For 10 points, name this caliphate with a capital in Egypt that took its name from Muhammad's daughter.
A ruler of this dynasty was advised by the Jew Yaqub ibn Killis and, according to legend, converted to Christianity after watching Simon the Tanner lift a mountain into the air. This dynasty's vizier Shawar used naphtha to burn one of its main cities after his repeated switching between alliances with Amalric I and Shirkuh led to invasions by both. A ruler of this dynasty forced Jews to wear bells and Christians to wear iron crosses, and disappeared into the desert years after (*) demolishing the Church of the Holy Sepulchre in Jerusalem. This dynasty included the "Mad Caliph," al-Hakim. This caliphate built its capital near al-Fustat and was eventually supplanted by Saladin's Ayyubid dynasty. For 10 points, name this caliphate with a capital in Egypt that took its name from Muhammad's daughter.
A ruler of this dynasty was advised by the Jew Yaqub ibn Killis and, according to legend, converted to Christianity after watching Simon the Tanner lift a mountain into the air.
Fatimid dynasty [or Fatimid caliphate]