Introduction to elliptic curves. Math 682
Homework 5. Due April 4, 2008
To get full credit solve 3 of the following problems (you are welcome to attempt them all)
1. (a) Find a set of generators for E(Q)/2E(Q) for E : y 2 = x(x2 + 3x + 5).
Hint: Look at t
Introduction to elliptic curves. Math 682
Homework 4. Due March 12, 2008
To get full credit solve 3 of the following problems (you are welcome to attempt them all)
1. (a) Consider the lattice = Z + iZ. Prove that g6 () = 0 but g4 () is a nonzero real
numb
Introduction to elliptic curves. Math 682
Homework 3. Due February 27, 2008
To get full credit solve 3 of the following problems (you are welcome to attempt them all)
1. For each of the following elliptic curves, determine all the points of nite order and
Introduction to elliptic curves. Math 682
Homework 1. Due January 28, 2008
To get full credit solve 5 of the following problems (you are welcome to attempt them all)
1. A natural number n is said to be congruent if it is equal to the area of a right trian
Introduction to elliptic curves. Math 682
Homework 2. Due February 6, 2008
To get full credit solve 4 of the following problems (you are welcome to attempt them all)
1. Find an equation in Weierstrass form for the projective elliptic curve X 3 + Y 3 Z 3 w