edge
渊 centers on a deep, still body of water: an abyss or deep pool. The given meaning 'edge' is unusual and may reflect a rare or extended usage; the primary idea is depth and stillness.
渊 is the simplified form of 淵. The traditional form combines 氵 (water) with a phonetic component that suggests deep water. The modern simplified right side is visually similar to 米 but is not historically related to rice.
The water radical 氵 on the left suggests a deep pool. The right side looks like a cross-shaped marker over a deep well, warning of the abyss below.
For エン, imagine standing at the edge of a deep pool and hearing a distant 'en' sound echoing from the abyss: en -> エン.