Finding rational points on elliptic curves using 6-descent and 12-descent
نویسندگان
چکیده
منابع مشابه
Finding Rational Points on Elliptic Curves Using 6-descent and 12-descent
We explain how recent work on 3-descent and 4-descent for elliptic curves over Q can be combined to search for generators of the Mordell-Weil group of large height. As an application we show that every elliptic curve of prime conductor in the SteinWatkins database has rank at least as large as predicted by the conjecture of Birch and Swinnerton-Dyer.
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In this paper, we discuss the information obtainable from descent via torsors under finite k-group schemes on the location of the k-rational points within the adelic points on a smooth projective k-variety X , where k is a number field. When X is a curve of genus ≥ 2, we conjecture that the information coming from “finite abelian descent” cuts out precisely the rational points; we provide theor...
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Let k be a number field and X a smooth projective k-variety. In this paper, we study the information obtainable from descent via torsors under finite k-group schemes on the location of the k-rational points on X within the adelic points. Our main result is that if a curve C/k maps nontrivially into an abelian variety A/k such that A(k) is finite and X(k, A) has no nontrivial divisible elements,...
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Let k be a number field and X a smooth projective k-variety. In this paper, we discuss the information obtainable from descent via torsors under finite k-group schemes on the location of the k-rational points on X within the adelic points. We relate finite descent obstructions to the Brauer-Manin obstruction; in particular, we prove that on curves, the Brauer set equals the set cut out by finit...
متن کاملInfinite Descent on Elliptic Curves
We present an algorithm for computing an upper bound for the difference of the logarithmic height and the canonical height on elliptic curves. Moreover a new method for performing the infinite descent on elliptic curves is given, using ideas from the geometry of numbers. These algorithms are practical and are demonstrated by a few examples.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2008
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2008.04.007