Looks like a very interesting hybrid/cross.
I'd say chinense crossed with baccatum (upright pods like baccatum, single pod, the height/growth, and the leaves look like a baccatum)
Is there any colour in the flowers? Baccatums usually have a bit of green/brown or yellow spotting.
Frutescens grow pods upright too, but pods smaller and leaves smaller.
If the flowers are plain white could be an odd annuum cross though, the extra purpling of the stems and leaves is more common on them. Though only on purple/dark pods before ripening (plant kind of also looks like a czech/hungarian black - but again with larger leaves than annuums - yours got baccatum/chinense sized leaves)
edit:
It's a 'bitzer', could be annuum/baccatum/chinense cross. How hot are the pods? If not that hot it may not even have any chinense in it at all. Though only you can say how hot the pods are and it' looks bumpy; I haven"t seen any bumpy baccatums/annuums....
Would help if there was some focused clear great photos of the flowers.