By BBC News –
A fourth defendant was sent to a juvenile detention centre by the court in the central province of Minya.
The teenagers argued they were mocking beheadings by the Islamic State group.
Egypt’s Christians have long complained of discrimination in the predominantly Muslim country.
The four teenagers were convicted by the court in the city of Beni Mazar on Thursday.
Security was stepped up around the court building, with a number of police vehicles reportedly deployed in the area.
Defence lawyer Maher Naguib described the verdict as “unbelievable”, saying he would appeal.
The video was published online last April – shortly after IS jihadists beheaded dozens of Egyptian Christians in Libya.
The student’s teacher, who filmed the video, was sentenced to three years in prison in a separate trial.
There have been a number of blasphemy cases in recent months.
In January, writer Fatima Naoot received a three-year prison term and a fine after being found guilty of contempt of religion.
A number of similar cases have been filed since the 2011 uprising, many of them against Copts, who make up about 10% of Egypt’s 82 million people.
Under Egyptian law, a person can be jailed for up to five years and fined for religious blasphemy.
Human rights groups have long campaigned for the abolition of this article from the country’s penal code.