A potato cultivar designated E12 is disclosed. The invention relates to the tubers of potato cultivar E12, to the seeds of potato cultivar E12, to the plants of potato E12, to the plant parts of potato cultivar E12, to food products produced from potato cultivar E12, and to methods for producing a potato plant produced by crossing potato cultivar E12 with itself or with another potato variety. The invention also relates to methods for producing a potato plant containing in its genetic material one or more transgenes and to the transgenic potato plants and plant parts produced by those methods. This invention also relates to potato cultivars or breeding cultivars and plant parts derived from potato variety E12, to methods for producing other potato cultivars, lines or plant parts derived from potato cultivar E12 and to the potato plants, varieties, and their parts derived from use of those methods. The invention further relates to hybrid potato tubers, seeds, plants and plant parts produced by crossing potato cultivar E12 with another potato cultivar.