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dc.contributor.authorBaker, Michael 13:32:02 (GMT) 13:32:02 (GMT)
dc.description.abstractLet $q$ 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.publisherUniversity of Waterloo
dc.subjectelliptic curvesen
dc.subjectmodular formsen
dc.subjectHurwitz class numbersen
dc.subjectquadratic formsen
dc.subjectmodular curvesen
dc.titleElliptic Curves over Finite Fields and their l-Torsion Galois Representationsen
dc.typeMaster Thesisen
dc.subject.programPure Mathematicsen Mathematicsen
uws-etd.degreeMaster of Mathematicsen

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