C.11 Examples for Chapter 21

Example 40

We want to graph the elliptic curve y2=x(x1)(x+1).

First, we create a string v that contains the equation we wish to graph.

>> v=’y^2 - x*(x-1)*(x+1)’;

Next we use the ezplot command to plot the elliptic curve.

>> ezplot(v,[-1,3,-5,5])

The plot appears in Figure C.1. The use of [1, 3, 5, 5] in the preceding command is to define the limits of the x-axis and y-axis in the plot.

Figure C.1 Graph of the Elliptic Curve y2=x(x1)(x+1).

A graph plots an oval shaped curve at the left along with an elliptic curve pointing towards right.

Example 41

Add the points (1,3) and (3,5) on the elliptic curve y2x3+24x+13(mod29).

>> addell([1,3],[3,5],24,13,29)

ans =
    26    1

You can ...

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