I'm studying the theory of elliptic curves and in all the books I've read they use the term "Weierstrass equation" or a similar one. But so far I've failed to find out when that term was used for the first time. In which Weierstrass' paper is included the general equation of an elliptic curve? Who was the first author to use that term to link the equation of an elliptic curve to Weierstrass?

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xyandyterms "generalized Weierstrass form". Since he uses the label "generalized", perhaps that means the terminology had not yet settled down. My hunch is that Weierstrass himself only worked with the equation $y^2 = 4x^3 - g_2x - g_3$, since that is satisfied by his $\wp$-function and its derivative, which is how he dealt with elliptic curves. Without arithmetic issues in mind, why look at something messier than $y^2 =$ cubic for ell. curves? – KConrad Jan 23 '13 at 22:28