The integer points on three related 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 ∆ = ...
متن کاملInteger points on two families of elliptic curves
In this paper we find all the integer points on elliptic curves induced by the Diophantine triples {k − 1, k + 1, 16k − 4k} and {k − 1, k + 1, 64k− 48k + 8k} that have either rank two or 2 ≤ k ≤ 10000 (with one possible exception).
متن کاملElliptic 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 (...
متن کاملThe distribution of the number of points modulo an integer on elliptic curves over finite fields
Let Fq be a finite field and let b and N be integers. We study the probability that the number of points on a randomly chosen elliptic curve E over Fq equals b modulo N . We prove explicit formulas for the cases gcd(N, q) = 1 and N = char(Fq). In the former case, these formulas follow from a random matrix theorem for Frobenius acting on the Ntorsion part of E, obtained by applying density resul...
متن کاملCOUNTING POINTS ON ELLIPTIC CURVES OVER F2n,
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1982
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1982-0658228-9