Montgomery normal form

The Montgomery normal form of an elliptic curve is a slightly different normalization from that of Weierstraß.

$by^{2}=x^{3}+ax^{2}+x$

It has in common with the Weierstraß normal form the same important property of being symmetric about the x-axis, and hence it is just as useful and possibly more convenient in some cases for computing the point group operation by using many if not most of the same techniques.