# Define an elliptic curve by its equation

Suppose we take the elliptic curve $E : y^2 = (ax+1)(bx+1)(cx+1)$ where $a,b,c \in \mathbb{Z}.$ We can define it by `E = EllipticCurve[a1,a2,a3,a4,a6]`

only if $abc = 1.$ Suppose $abc \neq 1$ then how to define it in its originality, i.e. without applying any co-ordinate transformations?