You can protect your Index Page and allow only logged in students to see it following these steps:
Go to your eLearn Commerce Settings.
Click Authentication Options from the General settings.
Under General Settings, click the Internal Auth Status drop-down and select Users are required to login in order to view the Index Page, Category Pages, Courses, Course ShortCode Embeds, Index Page Embeds, Videos.
Scroll down and click Save Changes.
You're all set!