transform into weierstrass-form

algebraic-geometry elliptic-curves

First change $y=2y'$ and $x=x'$. That will leave the model in the form $$y'^2 = (x'-e_1)(x'-e_2)(x'-e_3),$$ after cancelling $4$'s on both sides. Now expand the polynomial, in $x'$, so that you have $$y'^2 = x'^3+Ax'^2+Bx'+C.$$ Finally, a change of the form $x' = X-A/3$ and $y'=Y$ gets rid of the $X^2$ term, and leaves $$Y^2 = X^3+DX+E.$$

Related

The series expansion of $\frac{1}{\sqrt{e^{x}-1}}$ at $x=0$
Why degree of a reducible projective variety is the sum of the degree of its irreducible components
Graph of a continuous function is closed
Sum of the first $n$ triangular numbers - induction
How to prove that $\sum_{k=0}^n \binom nk k^2=2^{n-2}(n^2+n)$ [duplicate]
Proof of Pasting Lemma
"Real" cardinality, say, $\aleph_\pi$?
Define $S\equiv\{ x\in \mathbb{Q}\mid x^2<2\}$. Show that $\sup S=\sqrt{2} $.
$\epsilon - \delta$ proof that $\lim_{x \to a} \sqrt x = \sqrt a$
Finding the left and right cosets of $H=\{(1),(12),(34),(12) \circ(34)\}$ in $S_4$
Proving that the empty set is unique
Does the correctness of Riemann's Hypothesis imply a better bound on $\sum \limits_{p<x}p^{-s}$?