Data on elliptic curves with high rank

In this thesis, a map that takes points from a given Elliptic Curve in Weierstrass form to points on the corresponding curve in Hasse form was derived. This was implemented in the Maple programming language in order to allow the transformation of points into Hasse form so that an embedding into the space K*/K*3 x K*/K*3could be easily computed. The derivation of the map involved several intermediate maps as well as optimization techniques to facilitate feasible computations. The map was further used to embed points of height less than 50 into K*/K*3 x K*/K*3 and test whether the images are trivial, which gives information on how this set sits inside the space.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2004

Author dc:creator

• Khan, Siddique, 1980-

Advisor dc:contributor.advisor

• Catherine O'Neil.

• Electrical Engineering and Computer Science.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/28413

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/28413