Check out the excellent article, “IF I BE LIFTED UP” by Grace Roberta Wasson, from the July 1921 CS Journal: good explanation of how Christ reversed the curse.

Here is an excerpt:

“The Jewish patriarch came near confusing the Adam definition of serpent with the Christ definition, when God bade him cast his rod upon the ground and he saw it become a serpent. Moses fled from what he saw, but that which he saw was an hallucination. God bade him return and pick up the serpent. Moses’ obedience opened his eyes, gave him spiritual vision, which contradicted sense testimony, and he then knew that he had been subscribing to general belief which was absolutely false, regarding an expression of Deity. He learned that serpent, instead of being a dangerous, loathsome, writhing reptile, which he refers to in his Edenic allegory as “cursed above all cattle, and above every beast of the field,” was exactly the reverse of what he had supposed. This vision was to become enlarged, for in the twenty-first chapter of Numbers we read how, when the Hebrew pilgrims turned from God and cried out against the Almighty, the “fiery serpents” appeared among the people, “and they bit the people; and much people of Israel died.” Then, returning penitent, they besought Moses to ask God to forgive them for their sins, and God advised Moses accordingly and ‘Moses made a serpent of brass, and put it upon a pole, and it came to pass, that if a serpent had bitten any man, when he beheld the serpent of brass, he lived.’

“The serpent, as Satan’s tool, is a symbol of sin adjudged (or death, for the wages of sin is death), but when elevated or lifted up, as Moses did in two instances, it becomes the type of Christ. Brass speaks of judgment, as in the brazen altar of God’s judgment, and in the laver of self-judgment (Exodus 27). The brazen serpent is a type of Christ who was made ‘to be sin for us, who knew no sin,’ in bearing our judgment, for we are told in John’s gospel, that ‘as Moses lifted up the serpent in the wilderness, even so must the Son of man be lifted up: that whosoever believeth in him should not perish, but have eternal life.'” [emphasis added]