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 NmE and its peak height h(m)E are governed by the solarzenith angle chi in accordance with relations relations NmE alpha(cos chi)(p) and h(m)E alpha ln(sec chi), 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 degrees-10 degrees, and the other two with much wider latitude extent of about 10 degrees-20 degrees appear on both sides of the geomagnetic equator in latitude regions +/- 20 degrees-30 degrees, 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 chi and f(o)E (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.