The Galois Group of 8-Torsion Points on Elliptic Curves

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dc.contributorDavidoff, Giuliana
dc.contributorRobinson, Margaret
dc.contributor.advisorWeston, Tom
dc.contributor.authorJin, Kexin
dc.date.accessioned2017-07-05T13:17:03Z
dc.date.available2017-07-05T13:17:03Z
dc.date.gradyear2017en_US
dc.date.issued2017-07-05
dc.description.abstractIn this paper, we explore the Galois group of 8-torsion points on elliptic curves over Q. In particular, we present algorithms that allow us to find the subgroup of GL2(Z/8Z) that best represents the 8-torsion group of a fixed elliptic curve E. We first give a general introduction to elliptic curves, algebraic number theory, and representation theory, which together provide a theoretical background for computations. We present the algorithms at the end of the paper, along with some computational results of its application.en_US
dc.description.sponsorshipMathematics & Statisticsen_US
dc.identifier.urihttp://hdl.handle.net/10166/4073
dc.language.isoen_USen_US
dc.rights.restrictedrestricteden_US
dc.subjectElliptic Curvesen_US
dc.titleThe Galois Group of 8-Torsion Points on Elliptic Curvesen_US
dc.typeThesis
mhc.degreeUndergraduateen_US
mhc.institutionMount Holyoke College

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