Normal Forms for Elliptic Curves Sample Clauses

Normal Forms for Elliptic Curves. ‌ Before turning to the description of elliptic fibrations, let us look at the simpler setup of elliptic curves. Our first goal is to construct the Weierstraß equation for such curves, following [71,72]. That is, we aim to show that any elliptic curve (E, P ) – i.e. any projective non-singular curve of genus 1 with a specified point P – can be written as a hypersurface embedded in P[1,2,3] with projective coordinates w, x, and y, described by the Weierstraß equation
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