Integer points on elliptic curves
نویسندگان
چکیده
منابع مشابه
S-integer Points on Elliptic Curves
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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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 ...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2005
ISSN: 0030-8730
DOI: 10.2140/pjm.2005.222.237