In most situations, I would recommend trying to remote into the system, and see if you can see what processes are listening on those ports. That would give you the best idea of what is going on in the system (i.e. which processes are bound to those ports).
Since that does not appear to be an option for you, my next suggestion would be to monitor all traffic which is going into those ports using Wireshark or a similar protocol analyzer. You might be able to determine what those ports are doing based on the traffic going to them, and may even be able to capture some login credentials.
Given the fact that this is an LTE router, and you may not be able to perform a capture on those ports, my last suggestion would be to see if you can download a copy of the router's firmware from the internet. You can then analyze the firmware with a tool like binwalk. This is not a very reliable method, since there is no guarantee that the firmware on your router will match what was downloaded, but if you can't find those ports open on the downloaded image, you know something is odd about the firmware running on your router.