curl vs curl up

curl is a noun but curl up is not a noun.

Word	Noun	Adjective	Verb	Adverb
curl	Yes	No	Yes	No
curl up	No	No	Yes	No

As verbs, curl and curl up are synonyms defined as:

Other synonyms of curl include draw in.

curl (noun)	curl up (noun)
lock of hair in the shape of a spiral or curl
a round shape formed by a series of concentric circles (as formed by leaves or flower petals)

curl (verb)	curl up (verb)
form a curl, curve, or kink	shape one's body into a curl
play the Scottish game of curling
twist or roll into coils or ringlets
wind around something in coils or loops
shape one's body into a curl