Today we read about the abelian group that can be formed from the points on an elliptic curve. One thing that we learned was that the term elliptic curve is named such because the equations involved are also involved in computing the arc length of ellipses. This section was not to hard to understand, there is a little algebra when computing P1+P2, but not too bad. The next section looks worse, when you stsart creating these modular groups. The way I understand it, it appears that in a curve mod n you might have many more points than n, in fact, it looks like you have to have more points than n. Section 16.2.1 talks about this and I find it interesting.
Section 16.2.1 contradicts what I thought and the section after that gives a more precise method of predicting the number of points in E.
I forgot how to make a variable substitution to turn x^3+ax^2+bx+c into x^3+b'x+c'. It is taught in 372 I think. I will be taking that class next semester. I should look up the substitution.
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