ΔE 23.5, loose: different enough that you should pick on purpose. Alizarin Crimson is a little lighter, much more saturated, warmer than Encarmine Red.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 23). Alizarin Crimson is a little lighter, much more saturated, warmer than Encarmine Red.
The same difference applies the other way round: Encarmine Red is a little darker, much more muted, cooler.
ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.
See Encarmine Red on the colour wheel See Alizarin Crimson on the colour wheel
All matches: Encarmine Red equivalents · Alizarin Crimson equivalents