Legendre form of an elliptic curve
= Legendre form of an elliptic curve
{c}
{title2=$Y^2Z=X(X-Z)(X-\lambda Z),\quad\lambda\ne0,1$}
Over an <algebraically closed field> of characteristic different from two, a cubic <Weierstrass model> with distinct roots becomes this form by sending two roots to zero and one, then scaling $Y$ by a square root of the resulting nonzero coefficient. The third root becomes $\lambda\notin\{0,1\}$. The point $[0:1:0]$ is a <flex> and the curve is a <genus one curve>.