Air carrier First Officer reported receiving a low altitude alert from ATC on a visual approach to SLC.

Narrative

We were descending on the NORDK 6 Arrival into SLC in excellent VMC meteorological conditions. During the Approach Briefing; I had thoroughly covered the terrain surrounding SLC; and reviewed the Class B airspace page and Jepp pages 19-01 through 08. Our speed was 210 kts. assigned. The moon overhead was within three days of full phase; so the terrain was illuminated very well. After passing ANNTY; the Approach Controller asked if we had the airport in sight; to which the Captain replied yes. We were then cleared for the visual approach to Runway 34L. To my recollection; I have always been vectored to the final approach course in SLC; even in visual conditions. Due to that expectation bias; I was a little surprised when we were cleared for the visual approach. We were pretty high on the downwind. I called for flaps 5 and in concurrence with the Captain; I set 6100 ft. in the MCP altitude selector and planned my descent to cross FFLAG at 6100 ft. As mentioned; the terrain was very well illuminated; so I proceeded to descend on downwind and base while visually maintaining terrain clearance with the terrain display as an additional reference. I asked the Captain to select FFLAG to LSK 1 of the LEGS page for vertical reference in the descent. As I was initiating my turn to base leg; the Tower Controller issued an Altitude Alert. The Controller asked if we had the terrain in sight; to which the Captain replied that we did. We were visually well clear of terrain and had no terrain concerns shown on the terrain display. Again; as a backup reference only; the terrain display indicated green ahead of our planned flight path at all times. We continued the descent and crossed FFLAG at 6100 ft. The rest of the approach and landing was uneventful. Although we had visual reference with the terrain at all times; it was very unsettling to receive the altitude/terrain advisory. Had there been an RNAV RNP approach to Runway 34L; I definitely would have requested it. Under the circumstances; I would have preferred vectors to the final approach course; prior to being cleared for the visual approach. A better course of action would have been to ask the Captain to request vectors to the final approach course. I also probably should have angled my downwind a little further to the left while descending. I am always cautious and mindful of terrain; and thought that I was allowing for adequate clearance. Because this occurrence was unsettling to me; in future similar situations I intend to allow for even more terrain clearance and utilize RNAV RNP approaches when available or request vectors to final.