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OverviewLet E be an elliptic curve defined over a number field K. An element of the n-Selmer group of E can be represented as a geometric object. Namely, as an everywhere locally soluble genus one curve defined by an equation of degree n. This equation is a generalised binary quartic when n=2, a ternary cubic when n=3, and two quadrics in four variables when n=4. By minimising these equations we mean making their invariants as small as possible. Unfortunately, the minimal (with the smallest invariants) equations of degree n are not unique in general. We exploit the theory of minimal regular models to find an alternative definition of minimality. Then we use this new definition to count the minimal equations of degree n. Full Product DetailsAuthor: Mohammad SadekPublisher: LAP Lambert Academic Publishing Imprint: LAP Lambert Academic Publishing Dimensions: Width: 15.20cm , Height: 0.70cm , Length: 22.90cm Weight: 0.191kg ISBN: 9783843353847ISBN 10: 3843353840 Pages: 124 Publication Date: 13 September 2010 Audience: General/trade , General Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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