Prosecutors say Cortez, 43, had sex with two male students, who were 16 and 17 at the time, at her Montebello residence in 2009 and 2010.
Cortez was a teacher at Roosevelt High School in Boyle Heights. She was arrested in February. She was placed on leave after her arrest.
Cortez was free on bail Monday pending her scheduled sentencing in January.
The Associated Press contributed to this report.