Nikon 1 J4 has a Nikon 1 lens mount and currently there are 13 native lenses available for this mount.
Nikon 1 J4 doesn't have a sensor based image stabilization system but 7 of these lenses already comes with optical image stabilization.
Since Nikon 1 J4 has a 1 inch Sensor sensor, it has a focal length multiplier of 2.7× so you have to multiply lenses original focal length with this multiplier to find the Full Frame equivalent focal length of the lens when mounted on 1 J4.
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Nikon 1 J4 Lenses with Image Stabilization
Nikon 1 J4 Lenses with Weather Sealings