Rational Points on Elliptic Curves

Mishra, shubham and Kumar, Narasimha (2018) Rational Points on Elliptic Curves. Masters thesis, Indian Institute of Technology Hyderabad.

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Abstract

The aim of this thesis is to de�ne the Elliptic Curves and some of intresting properties of a special class of terms,namely,rational point of elliptic curve ,The properties of the rational pooint of curve is airthmetic ,and rational point on elliptic curve forms a �nitely generated group structure group it will be done by using the chord-tangent group law of composition.After completing the the abelian group structure,so we look some elementary properties like for a given elliptic curve we �nd the torsion subgroup of that elliptic curves.and �nally done the elliptic curve and their isomorphism. Further, we study different families of elliptic curves which depend on different parameters. Moreover, we look at the reduction modulo p of an elliptic curve and infer the meaning of good and bad reduction of an elliptic curve. Lastly, the statement and proof of Mordell-Weil theorem is given. The topics of the thesis are based on the book Elliptic Curves by Dale Husemoller. I have not added anything new, except making a few observations of my own.

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IITH Creators:
IITH CreatorsORCiD
Kumar, NarasimhaUNSPECIFIED
Item Type: Thesis (Masters)
Uncontrolled Keywords: Elliptic Curves
Subjects: Mathematics
Divisions: Department of Mathematics
Depositing User: Team Library
Date Deposited: 06 Jun 2018 10:31
Last Modified: 06 Jun 2018 10:31
URI: http://raiith.iith.ac.in/id/eprint/3998
Publisher URL:
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