All scrolls cast at level 5 and at their rank. That means- base scrolls at B5,
- expert scrolls at E5,
- master scrolls at "M5" even if M5 isn't possible otherwise,
- grandmaster scrolls at "G5" even if G5 isn't possible otherwise.
Therefore, the beacon cast from a scroll should last 35 days. Note though, that your chance to get the scroll from the dragon is null, point, bags of nulls, even more nulls, nothing. I have played the game uncountably many times and (since I have found out how to kill the dragon) I have always multiloot the dragon. In all my experience, I have seen the scroll only *once*.
Therefore, don't count on getting the scroll from the dragon and forget returning on EI. No chance.