# Given a real number, how do I produce an elliptic curve with j-invariant equal to that number?

I have formula for computing the j-invariant but I was wondering if given number $j$, is there a formula for getting a curve $y^2=x^3+a_2x^2+a_4x+a_6$ with j-invariant j?

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This construction works unless $j=0$ or $j=1728$. But $y^2+y=x^3$ has $j=0$, and $y^2=x^3+x$ has $j=1728$. –  Álvaro Lozano-Robledo Apr 15 '13 at 13:35