Data on elliptic curves with high rank
Author(s)Khan, Siddique, 1980-
Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.
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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.
Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Includes bibliographical references (leaf 43).
DepartmentMassachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.
Massachusetts Institute of Technology
Electrical Engineering and Computer Science.