Lie rings of prime-square order

The list
Let $$p$$ be a prime number. There are, up to isomorphism, three Lie rings whose order is $$p^2$$:

(The numbers assigned here are local, for internal reference in this article; there is no standard enumeration of the Lie rings of prime-square order that is analogous to the GAP Group ID)

For a proof, see classification of Lie rings of prime-square order.