dc.contributor.author Baker, Michael dc.date.accessioned 2015-09-08 13:32:02 (GMT) dc.date.available 2015-09-08 13:32:02 (GMT) dc.date.issued 2015-09-08 dc.date.submitted 2015-08-25 dc.identifier.uri http://hdl.handle.net/10012/9649 dc.description.abstract Let $q$ and $\ell$ be distinct primes. Given an elliptic curve $E$ over $\mathbf{F}_q$, we study the behaviour of the 2-dimensional Galois representation of $\mathrm{Gal}(\overline{\mathbf{F}_q}/\mathbf{F}_q) \cong \widehat{\mathbf Z}$ on its $\ell$-torsion subgroup $E[\ell]$. This leads us to the problem of counting elliptic curves with prescribed $\ell$-torsion Galois representations, which we answer for small primes $\ell$ by counting rational points on suitable modular curves. The resulting exact formulas yield expressions for certain sums of Hurwitz class numbers. en dc.language.iso en en dc.publisher University of Waterloo dc.subject elliptic curves en dc.subject modular forms en dc.subject Hurwitz class numbers en dc.subject quadratic forms en dc.subject modular curves en dc.title Elliptic Curves over Finite Fields and their l-Torsion Galois Representations en dc.type Master Thesis en dc.pending false dc.subject.program Pure Mathematics en uws-etd.degree.department Pure Mathematics en uws-etd.degree Master of Mathematics en uws.typeOfResource Text en uws.peerReviewStatus Unreviewed en uws.scholarLevel Graduate en
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