How to find out what carrier my iPhone belonged to?

I have a Black factory unlocked iPhone 5 on AT&T. I want to know what carrier it was bought from to configure my APN settings to receive LTE, my plan has LTE but I only get 4G. LTE is switched on in the settings and I've had the phone for a month, I had a white iPhone 5 that i switched for my black on with some one on craigslist. My old iPhone had LTE just fine. So what can I do?

Http://www.imei.info/

You can try there. Enter your IMEI and it will give your phone's info. Maybe the LTE band is not compatible with your network. The APN should come from your carrier though not the original carrier.

If the phone is factory unlocked, it never had a carrier. It would have been purchased directly from Apple.