The 50 AE uses .500" diameter projectiles.
.510 bullets for the various Linebaugh, 50-70 Government, 50 Alaskan, 500 A-Square, etc. are NOT what you want.
Barnes offers "solid" projectiles in .500 from 275-375g designed for the 500 S&W. The position of the cannelure may restrict their use in the 50 AE. I'd call and ask them before paying the price of admission.
Dave at Lehigh also offers a .500 solid, 363g again designed for the 500 S&W and 50 Beowulf. It has multiple pressure bands which may work a little easier in seating and crimping in the 50 AE.
I have little use for a solid projectile in the 50AE. The Sierra 350g HP works fine for everything I'd use it for.
If you're wanting to punch .510 holes in things, look at a 50-70 Government, 500 Alaskan or 500 BFG throated for BMG projectiles - they'll shoot everything from the 325g Barnes to the 750g Hornady AMAX with the proper barrel twist.