at the time/ strange conjectures

Would you tell me whether I am right with my interpretation of the expression in bold in the following sentences?

In the center of the room, clamped to an upright easel, stood the full-length portrait of a young man of extraordinary personal beauty, and in front of it, some little distance away, was sitting the artist himself, Basil Hallward, whose sudden disappearance some years ago caused, at the time, such public excitement, and gave rise to so many strange conjectures. (Oscar Wild, “The Picture of Dorian Gray”)

I was ill at the time.

I didn’t know it at the time.

at the time = then

strange conjectures = fantastic/ whimsical conjectures

Thank you for your efforts.