"It has always been a strong goal of the JPEG committee that its standards should be implementable in their baseline form without payment of royalty and license fees... The up and coming JPEG 2000 standard has been prepared along these lines, and agreement reached with over 20 large organizations holding many patents in this area to allow use of their intellectual property in connection with the standard without payment of license fees or royalties." (Wikipedia)

So yes it's patent-encumbered but no more patent-encumbered than WebP.

https://chromium.googlesource.com/webm/libwebp/+/master/PATE...

That statement is AFAIK now absent from the JPEG site.

On the positive side, it's now old enough that some key patents (e.g. arithmetic coding) have actually expired.