The purpose of this study is to explore how the elements of synchronous online learning emerge in mathematics classroom discourse through an authority lens. To this end, we analyzed synchronous online learning classes for 5th to 6th graders. Elements of synchronous online learning were divided into delivery system, interaction, content, and learners; and data modeling tasks were implemented. Findings indicate that the delivery system has both potential and risk for sharing authority in mathematics classroom discourses, and four types of interactions are formed (or not formed) in a differentiated manner, respectively. In addition, mathematics classroom discourses, such as providing teacher feedback and encouraging students supported students' shared authority. Further, the content element combined with other elements, was found to influence sharing authority. These findings reveal some aspects that teachers should consider in designing and implementing synchronous online learning for shared authority.