Titlebook: Elliptic Curves over Number Fields with Prescribed Reduction Type; Michael Laska Book 1983 Springer Fachmedien Wiesbaden 1983 Algebra.Endl

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,The diophantine equation x3 ? y2 = r,with good reduction outside SS., where S. is some set of prime divisors of 2 or 3 in ., satisfy certain additional conditions (see Corollaries 2.10 and 2.11, see also 2.12) and hence for the construction of these curves the above equation need not be solved completely. In the present chapter we deal now with the construction of the set B..

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Introduction,es over K (for the definitions see chapter 1). Moreover, for a given ideal a in . the number of isogeny classes of elliptic curves over K with conductor a is finite. In these notes we deal with the following .: How can one explicitly construct a set of representatives for the isogeny classes of elli

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,The diophantine equation x3 ? y2 = r,reduction outside S from a set B. of representatives of non-associated basic solutions of the exponential diophantine equation.where S = {η., ..., η.} (see Theorem 2.4). For that we had to assume that every prime divisor of 2 or 3 is contained in S. Solutions in B. that give rise to elliptic curves

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Review on Explicit Results,xplicitly been determined for several concrete choices of K and S. In most cases .(S) is obtained by implementing the three steps stated in the introduction. In this chapter we give a review on these and related results.

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Three-Dimensional Coordinate Geometry,ics, chemistry, and industry, without compromisingtheir accuracy. It exploits the full potential of the dimensionlessrepresentation of these models by considering the special nature ofthe characteristic dimensionless quantities. It can be argued thatthese dimensionless quantities mostly assume extre

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Variation in female mate choice within guppy populations: Population divergence, multiple ornamentsview recent work on variation within and among guppy (.) populations in female mate choice and mating preferences. Empirical results demonstrate that there is substantial variation within and among populations in female responsiveness and choosiness, and much of this variation is genetic. Evidence f