CLehnert on "Need to Remove Login and Lost Password Links from beneath "Register" form"

Most importantly, I need to remove the "Login" link that appears below the "Register" form. Strangely, I can use this to remove the "Register" link from below the login page, but it does not work to remove anything from the Register page:

add_filter('register', 'remove_links');
		function remove_links() {
			unset($login_url);
		}

Is there any type of filter or hook I can use to remove these two links? I need to make sure only the registration form is available to prevent malicious users from accessing the login form. Any help here is greatly appreciated.
CSS display: none will not be sufficient, because the links are actually still accessible in the page, just not visible. Removing them with jQuery is also not ideal, because this can be circumvented.
Thanks