منابع مشابه
Elliptic Nets and Points on Elliptic Curves
(2) hn divides hm whenever n divides m. They have attracted number theoretical and combinatorial interest as some of the simplest nonlinear recurrence sequences (see [3] for references), but for us their interest lives in the underlying geometry: Ward demonstrates that an elliptic divisibility sequence arises from any choice of elliptic curve over Q and rational point on that curve. Theorem 1 (...
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We give a quantitative bound for the number of S-integral points on an elliptic curve over a number field K in terms of the number of primes dividing the denominator of the j-invariant, the degree [K : Q], and the number of primes in S. Let K be a number field of degree d and MK the set of places of K. Let E/K be an elliptic curve with quasi-minimal Weierstrass equation E : y = x +Ax+B. If ∆ = ...
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In this paper we present an implementation of Schoofs algorithm for computing the number of i"2m-P°mts °f an elliptic curve that is defined over the finite field F2m . We have implemented some heuristic improvements, and give running times for various problem instances.
متن کاملReductions of Points on Elliptic Curves
Let E be an elliptic curve defined over Q. Let Γ be a subgroup of rank r of the group of rational points E(Q) of E. For any prime p of good reduction, let Γ̄ be the reduction of Γ modulo p. Under certain standard assumptions, we prove that for almost all primes p (i.e. for a set of primes of density one), we have |Γ̄| ≥ p f(p) , where f(x) is any function such that f(x) → ∞, at an arbitrary slow ...
متن کاملComputing Integral Points on Elliptic Curves
By a famous theorem of Siegel [S], the number of integral points on an elliptic curve E over an algebraic number field K is finite. A conjecture of Lang and Demjanenko [L3] states that, for a quasiminimal model of E over K, this number is bounded by a constant depending only on the rank of E over K and on K (see also [HSi], [Zi4]). This conjecture was proved by Silverman [Si1] for elliptic curv...
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ژورنال
عنوان ژورنال: Algebra & Number Theory
سال: 2009
ISSN: 1937-0652
DOI: 10.2140/ant.2009.3.283