It was a regular mail to my home with a nice folder about lifestyle benefits (very similar to the benefits for Amex Platinum). However, no word about benefits with SAS. The cost for the card is 3500 SEK per year and this fee is not waived even if you are a Platinum card member. They only give the basic SAS card for free to Platinum card holders.
The Amex representative I talked to said there are benefits with SAS with the Elite card but she didn't know what they are.