THE l-ADIC GALOIS REPRESENTATION ASSOCIATED TO AN ELLIPTIC CURVE
نویسنده
چکیده
Now let (x, y, z) be a representative of a class in E and suppose z 6= 0 then (xz , y z , 1) is the unique representative of [(x, y, z)], the class of (x, y, z), in the plane z = 1. So we can think of projective points on E with nonzero z-coordinate as corresponding bijectively to solutions (x, y) of y = x + ax + b. Now suppose z = 0, then [(x, y, z)] ∈ E implies that x = 0, so there is exactly one such class, it is [(0, 1, 0)]. When looking at the curve in affine coordinates, we will call this class O, the point at infinity.
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