DUE WEDNESDAY, NOVEMBER 14

**William Stein**

*Date:* **Math 124** HARVARD UNIVERSITY **Fall 2001**

- 1.
- (10 points) For any negative discriminant , let denote
the finite abelian group of equivalence classes of primitive positive
definite quadratic forms of discriminant . Use the PARI program
`forms.gp`from lecture 24 (download it from my web page) to compute representatives for and determine the structure of as a produce of cyclic groups for each of the following five values of : - 2.
- (6 points) Draw a beautiful graph of the set
of real
points on each of the following elliptic curves:
- (i)
- ,
- (ii)
- ,
- (iii)
- .

- 3.
- (4 points) A rational solution
to the equation
is .
Find a rational solution with
by drawing the tangent line to and
computing the third point of intersection.

William A Stein 2001-11-11