5 Elliptic curves
Johann Carl Friedrich Gauss (1777–1855) showed that the complex numbers ℂ can be identified with the plane ℝ × ℝ. By contracting the infinitely far border of this plane to a single point, we obtain the surface of a sphere. The extra point in the drawing corresponds to the North Pole and the real numbers together with this point appear as a circle on the sphere.
The typical shape of an elliptic curve over ℂ is more complicated and it emerges when we consider a grid. In the simplest case, this is the additive subgroup L = ℤ+ iℤ. For the grid L, we can form the quotient group ℂ/L. We can visualize this group as a three-dimensional ...
Get Discrete Algebraic Methods now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
