It was probably the 540s and the subsequent century or so.

> there were NO places in Europe where science or scholarship really flourished.

If you define ~800 AD as the end of the dark ages then yes. By Charlemagne’s time that had already changes.

It wasn’t exactly flourishing in Gaul, and Germany during the Roman times either. Those regions had arguably surpassed their Roman peak by the end of the dark ages.

And of course science and scholarship were preserved in Constantinople during the entire period (of course they had some very dark moments too)