Elliptic curves can be represented in different form. The most basic equation, in which every elliptic curve can be represented is the Weierstraß equation:
$$ y^2 = x^3 + ax + b$$
For a Montgomery curve it must be able to be represented in the following form:
$$ (b)y^2 = x^3 + ax^2 + x$$
For every Montgomery curve it is possible to transform its equation to ...