The short Weierstrass form is a specific way of representing elliptic curves using a simplified equation, typically expressed as $$y^2 = x^3 + ax + b$$, where $a$ and $b$ are constants that determine the shape of the curve. This form is particularly useful because it allows for easier computations and a clearer understanding of the properties of the elliptic curve, including its group structure and the behavior of its points. It provides a standard way to analyze elliptic curves in the context of algebraic geometry.
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