I thought that was a very good introduction to elliptic curves. I did not realize that the form for an elliptic curve was y^2=x^3+... They only showed a couple of graphs of what elliptic curves can look like. I know that they said that it only makes sense graphically in the rationals or reals, but could you show more example graphs of elliptic curves in class so we could have an idea of the different possibilities they can look like.
The book said that elliptic curves can be thought of rational points, reals, or even mod p. Can you have elliptic curves in the complex plane? The book did not mention that. Would the form still be the same as a standard elliptic curve and would it look the same, too?
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