I'm studying about elliptic curves. I'm reading Silverman's book, The Arithmetic of Elliptic Curves. I already asked things here and I was able to advance a little. I read in chapter III that a Weierstrass equation, through variable changes can be written in the form:
$y^{2}=4x^{3}+b_{2}x^{2}+2b_{4}x+b_{6}$
But a friend showed me Silverman's book Rational Points on Elliptic Curves, where it is written in session 1.3 that:
"we will restrict attention to cubics that are given in Weierstrass form, which classically consists of equations that look like
$y^{2} = 4x^{3} − g_{2}x − g_{3}.$
We will also use the slightly modified and more general equation
$y^{2} = x^{3} + ax^{2} + bx + c$,
and we will call either of them Weierstrass form."
My question is: is it possible to go from the equation
$y^{2} = x^{3} + ax^{2} + bx + c$
for the equation
$y^{2} = 4x^{3} − g_{2}x − g_{3}.$ ?