How to generate an elliptic curve in Sage
The list is a list of coefficients: [0,a,0,b,c] for y^2 = x^3 + ax^2 + bx + c.
You can put the field of definition in the first spot, e.g. GF(7) or RR or QQ
Get the points of your elliptic curve
The point (x,y) is written as (x:y:1) and the point at infinity is (0:1:0).