منابع مشابه
Visibility of Mordell-Weil Groups
We introduce a notion of visibility for Mordell-Weil groups, make a conjecture about visibility, and support it with theoretical evidence and data. These results shed new light on relations between Mordell-Weil and Shafarevich-Tate groups. 11G05, 11G10, 11G18, 11Y40
متن کاملDiscrete Logarithms and Mordell-Weil Groups
Let Ep be an elliptic curve over a prime finite field Fp, p ≥ 5, and Pp, Qp ∈ Ep(Fp). The elliptic curve discrete logarithm problem, ECDLP, on Ep is to find mp ∈ Fp such that Qp = mpPp if Qp ∈ 〈Pp〉. We propose an algorithm to attack the ECDLP relying on a Hasse principle detecting linear dependence in Mordell-Weil groups of elliptic curves via a finite number of reductions.
متن کاملOn certain sequences in Mordell–Weil type groups
In this paper we investigate divisibility properties of two families of sequences in the Mordell–Weil group of elliptic curves over number fields without complex multiplication. We also consider more general groups of Mordell–Weil type. M. Ward ([W], Theorem 1.) proved that a linear integral recurring sequence of order two which is not nontrivially degenerate has an infinite number of distinct ...
متن کاملSingular Plane Curves and Mordell-Weil Groups of Jacobians
This note explores the method of A. Néron [5] for constructing elliptic curves of (fairly) high rank over Q . Néron’s basic idea is very simple: although the moduli space of elliptic curves is only 1-dimensional, the vector space of homogeneous cubic polynomials in three variables is 10-dimensional. Therefore, one can construct elliptic curves which pass through any given 9 rational points. Wit...
متن کاملClassifying Brumer’s quintic polynomials by weak Mordell-Weil groups
We develop a general classification theory for Brumer’s dihedral quintic polynomials by means of Kummer theory arising from certain elliptic curves. We also give a similar theory for cubic polynomials.
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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2009
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crelle.2009.039