Is my coach love perfume real?

Hi, can someone help me out?

I bought a Coach Love perfume from Amazon, but the batch code is not appearing on Check Fresh. 😞

Is it possible for it to just not be there and for it to be real? I payed 50 bucks for it.

The batch code is AER36R206

Please help a woman that bought her dream perfume and thinks it’s not real 😞🙏🏻