2026-09-20T11:15:48Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/284132022-01-13T07:54:29Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Catherine O'Neil.
Khan, Siddique, 1980-
Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2005-09-26T20:18:41Z
2005-09-26T20:18:41Z
2004
2004
http://hdl.handle.net/1721.1/28413
56986160
Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.
Includes bibliographical references (leaf 43).
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.
by Siddique Khan.
M.Eng.
43 leaves
1014152 bytes
1016928 bytes
application/pdf
application/pdf
en_US
Massachusetts Institute of Technology
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.
http://dspace.mit.edu/handle/1721.1/7582
Electrical Engineering and Computer Science.
Data on elliptic curves with high rank
Thesis
application/pdf
false
Publication
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="e59a230d-d20c-4d63-964a-320252d8aa91">
<Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type>
<Language>en_US</Language>
<Title>Data on elliptic curves with high rank</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2004</PublicationDate>
<Authors>
<Author>
<DisplayName>Khan, Siddique, 1980-</DisplayName>
<Affiliation>
<OrgUnit>
</OrgUnit>
</Affiliation>
</Author>
</Authors>
<Editors>
</Editors>
<Publishers>
<Publisher>
<DisplayName>Massachusetts Institute of Technology</DisplayName>
<OrgUnit />
</Publisher>
</Publishers>
<License>http://dspace.mit.edu/handle/1721.1/7582</License>
<Keyword>Electrical Engineering and Computer Science.</Keyword>
<Abstract>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.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>