Rational Points on Elliptic Curves by Joseph H. Silverman & John T. Tate

Author:Joseph H. Silverman & John T. Tate
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

4.6 Exercises

4.1. Let p ≠ 2 be a prime, let satisfy acd ≠ 0, and let C be the conic given by the homogeneous equation

(a)If b 2 ≠ 4ac, prove that .

(b)If b 2 = 4ac, prove that either

Give examples for p = 3 to show that both possibilities can occur. More generally, show that both possibilities occur for all odd primes.

4.2. Compute the group for the curve

and the primes p = 3, 7, 11, and 13.

4.3. Let p ≥ 3 be a prime, and let m ≥ 1 be an integer that is relatively prime to p − 1. (a)Prove that the map is an isomorphism of to itself.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.