  An endo-commutative algebra is a nonassociative algebra in which the square
mapping preserves multiplication. In this paper, we give a complete
classification of endo-commutative curled algebras of dimension 2 over an
arbitrary non-trivial field, where a curled algebra satisfies the condition
that the square of any element is a scalar multiple of that element. We list
all multiplication tables of the algebras up to isomorphism.
