Cerebral amoebiasis is not caused by
Three free living amoebae are neuropathogenic (encephalitis)

Naegleria fowleri causes primary amoebic meningoencephalitis.  
Acanthamoeba causes granulomatous amoebic encephalitis.
Balamuthia mandrillaris causes amoebic meningoencephalitis.
Naegleria
Acanthamoeba
Dientamoeba
Balamuthia