From global measurements of ionospheric electron density profiles made by the FORMOSAT-3/COSMIC satellites, the morphology of E region electron density is investigated. Seasonal, latitudinal, and diurnal variations in daytime E region electron density are well described by the Chapman theory, and the E layer peak electron density N_mE and its peak height h_mE are governed by the solar zenith angle χ in accordance with relations N_mE $\propto$(cosχ)^p and h_mE $\propto$ln(secχ), respectively. However, it is revealed that there are three geomagnetic latitude regions where striking enhancements of the E region electron density occur. One of them is located at the geomagnetic equator with relatively narrow latitude extent of about 6°–10°, and the other two with much wider latitude extent of about 10°–20° appear on both sides of the geomagnetic equator in latitude regions ±20°–30°, respectively. The locations of these E region density enhancements are asymmetrical about the geomagnetic equator in solstice seasons, and they have a salient tendency to shift toward (away from) the summer (winter) hemisphere. The off-equator E region electron density enhancements are closely connected with the bottomside of the F region equatorial anomaly crests, where the component of the electron density parallel to the magnetic field line is maximum. It appears that the off-equator E region electron density enhancements are very likely the footprints of the F region equatorial anomaly crests. The morphologies of the exponent n and coefficient K in the power law relation between χ and f_oE (E region critical frequency) are also examined. There is a tendency for the n and K values to be larger in local winter than in local summer seasons in the latitudinal regions the same as the off-equator electron density enhancements. In addition, it is found that a minor peak in the K values is nearly continuously present in all seasons over the geomagnetic equator. A comparison shows significant discrepancies in the E region electron density morphologies between COSMIC measurement and IRI model prediction. Furthermore, compelling evidence is provided to show the presences of longitudinal wave number 3 and 4 structures of the electron density in the height region 100–200 km, which are in coincident with the longitudinal structures of equatorial electrojet. It is believed that these longitudinal 3- and 4-peak structures are very likely associated with nonmigrating diurnal tides propagating eastward in ionospheric E region.