Consider a general elliptic curve of the form $y^2=x^3+ax+b$, where $a,b\in\Bbb{C}$. These set of notes say that embedding this curve in $\Bbb{CP}^2$ make the zero set look like a torus. I am looking for an explanation of this. Thanks!
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1See this and this – reuns Aug 10 '17 at 13:00
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1In the first chapter of Kendig's Elementary Algebraic Geometry (Springer GTM Series #44) there are plenty of pictures and explanations that allow you to "see" this (without understanding the parametrization using Weierstrass $\wp$-function and its derivative). – Jyrki Lahtonen Aug 10 '17 at 13:04
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Does this answer your question? Torus and Elliptic curves – Max Demirdilek Mar 04 '23 at 21:25