Astronomers classify elliptical galaxies by

a. the number of stars they contain
b. their colors
c. how flattened they appear
d. their diameters

Astronomers classify galaxies according to Hubble's classification into elliptical, spiral and irregular, being the first two classes the most frequent.  

In the specific case of Elliptical galaxies, their main characteristic is that the concentration of stars decreases from the nucleus, which is small and very bright, towards its edges. In addition, they contain a large population of old stars, usually little gas and dust, and some newly formed stars.  

They are subdivided into eight classes, from E0 with zero eccentricity (spherical) to E7 (called husiform).  

However, it should be noted that this classification is based only on the visual appearance of the galaxy, and does not take into account other aspects, such as the rate of star formation or the activity of the galactic nucleus.  

Therefore, astronomer's clasification for elliptical galaxies is by their shape, which in this case is how flattened they appear.

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