I think it's just f10.
I use Alt-f10 to take a video with Shadowplay and I've not changed any defaults.
Screenshots are found here:
C:\Users\******Username******\Saved Games\Frontier Developments\Elite Dangerous\Screenshots
They're bitmaps .bmp so load them into Paint and just resave them again as a JPEG if you're posting them anywhere. Drops the filesize by about a factor of 10.
Thanks for reminding me - I'll have to rebind Shadowplay!