Weierstrass form

• Specific representation of an elliptic curve
• a way to represent an elliptic curve equation in a standardized form
• $y^2=x^3+ax+b$
  • y and x are the coordinates of points on the curve
  • Constant $a$ determines the slope of the tangent line at the point of infinity on the curve
  • Constant $b$ determines the y-coordinate of the point of intersection of the curve with the y-axis
• Has the presence of a distinguished point called the point at infinity, which serves as the identity (neutral) element for the group law operation on elliptic curves
• Group law is a key operation used in elliptic curve cryptography, which is a widely used cryptographic technique for secure communication and digital signatures
• Used to define an elliptic curve over different fields, such as the real numbers, complex numbers, or finite fields
• EFD / Genus-1 large-characteristic / short Weierstrass curves
• EFD / Genus-1 large-characteristic / Projective coordinates for short Weierstrass curves