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
(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.
Edit: Just realised this was posted in 2019.