What Is a “Stableswap” Curve and How Does It Modify the X Y = K Relationship?

A stableswap curve, pioneered by Curve Finance, is an AMM invariant designed for pegged assets like stablecoins. It modifies the constant product formula by incorporating an "amplification factor" (A) into a hybrid function.

The function is close to a linear relationship (x + y = k) near the peg, offering very low slippage. When the prices diverge significantly, the curve reverts to the standard constant product formula (x y = k) to maintain the invariant and prevent pool depletion.