Math 582: computational number theory
Homework 4 -- due by Friday Feb 5 at 9am
WARNING: I haven't exactly tried the problems below. I don't know how computationally difficult they are for sure.
Problem 1: Let denote the mod 2 representation attached to for each of the following elliptic curves: 17a1, 32a1, 32a2, 37a1. For each, compute explicitly the matrix of , where is a choice of prime ideal over each of 3,5,7,11,13. Be sure to check that is the charpoly of .
Problem 2: Let denote the mod 4 representation attached to for the curve 32a1. This is the homomorphism defined by the action of on . Be sure to check that is the charpoly of .
Try to compute explicitly the matrix of , where is a choice of prime ideal over each of 3,5,7,11,13.