The harsh ruling, which has followed a surge of blasphemy cases in Egyptian courts, underscores a culture of intolerance within the country's judicial system at a time when the Egyptian president is seeking to position himself as an advocate for religious reform.
Their teenagers' lawyer, Maher Naguib, said his clients, who are high school students in the southern province of Minya, haven't been detained and didn't appear in court for the trial.
The 30-second video showed the students pretending to pray, with one kneeling on the floor while reciting Qur'anic verses and two others standing behind him and laughing. One waved his hand under a second's neck in a sign of beheading.
Some ten security trucks surrounded the court building in the southern city of Bani Mazar. The families of the students cried, and some women wailed in disbelief and collapsed on hearing the verdict.
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The video prompted calls by angry Muslims to evict the students and the teacher from their village. They were detained and the teacher and his family were ordered to leave the village after a meeting of the village elders.
Christians make up approximately 10 percent of Egypt's population. They have long complained of discrimination by the Muslim majority.
Christians were among the main supporters of the army chief-turned-president, Abdel-Fattah el-Sissi, who led the military ouster of Islamist President Mohammed Morsi amid mass protests against Morsi's rule.