I understand, on a layman's level, Fray's motivation to write an elliptic equation corresponding to an assumed solution to FLT. My question is, how technically is Frey's equation derived?
$1.$ FLT : Contradiction. There exist integers $A,B,C,n>2$ such that $A^n + B^n = C^n$
$2.$ Frey: $y^2 = x(x-A^n)(x+B^n)$
$3.$ Elliptic curve $y^2= x^3 + ax + b$
$4.$ The curve is not modular. => not elliptic => FLT proved.
I need is the algebra to go from 1. to 3. above.
Assume Numbers A,B,C such that A^n + B^n = C^n contradicting FLT.
$y^2 = x^3 + ax + b$ an elliptic curve in Weirstrass form. I am guessing A and B go unchanged into x(x-A^n)(x+B^n)
Is that correct ?
Expanding 2. I get a term in x^2 , there is none in 3. This is my problem.
What does a $2$ dimensional graph of the Frey curve look like ?