Oscillatoria Vaucher ex Gomont

 From Latin oscillator, "something that swings"
 
This genus is named for the gliding, rotating, or oscillating motion of the filament around its axis. The trichomes are straight, slightly undulating, or coiled, and are made up of disk-shaped cells wider than they are long. In some species the end cells
can be rounded or tapered. The cells do not have gas vesicles, but sometimes contain large granules.
 
Unlike Lyngbya and Phormidium, Oscillatoria does not usually have a true sheath, although parallel filaments may form a thin film. Mucilage sheaths may also occasionally form under stressful conditions, such as dessication or hypersalinity, or in culture. Oscillatoria is also closely related to the genera Planktothrix, Limnothrix, Tychonema, and Trichodesmium. Several former species of Oscillatoria with thinner filaments and differences in morphology are now classified as species of Planktothrix, Pseudanabaena, or Limnothrix.

 
Oscillatoria culture specimens did possess sheaths (arrow).