I prefer a more generic form:

(y-a)(y-b) = (x-c)(x-d)(x-k)

By varying terms on both sides or making a term as a constant, you get generalizations for conics etc.

Dr Cook has been smashing out some excellent very digestible math content lately.

Edit: Just realised this was posted in 2019.

Ola

Nice explanation of elliptic curves especially the emphasis on how the underlying field changes what the curve actually is. The transition from intuitive equations to the formal definition (smooth, projective genus one) is very well done and the Curve1174 example helps clarify why not all elliptic curves look like Weierstrass forms

If folks have ever seen “ed25519” - say when generating an ssh key

https://en.wikipedia.org/wiki/EdDSA