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Normal form for Cubic 
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#1
Aug811, 05:32 PM

P: 348

Is there an algorithmic way to put a given elliptic curve into Weierstrass normal form? If not, what's the general procedure?



#2
Aug811, 08:15 PM

Mentor
P: 18,047

By changing coordinates, you get an equation of the form [itex]xy^2+(ax+b)y=cx^2+d+e[/itex] Multiply by x and change into the variable u=xy. This will get you something of the form [tex]u^2+(ax+b)u=cx^3+dx^2+ex[/tex] Change the variable again by setting [itex]v^2=u^2+(ax+b)[/itex]. Now change the variables once more to obtain that c=1. 


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