so-called vs alleged

so-called and alleged both are adjectives.

Word	Noun	Adjective	Verb	Adverb
so-called	No	Yes	No	No
alleged	No	Yes	No	No

As adjectives, so-called and alleged are synonyms defined as:

Other synonyms of so-called include supposed.

so-called (adjective)	alleged (adjective)
doubtful or suspect	declared but not proved
	doubtful or suspect