Large integral points on elliptic curves
نویسندگان
چکیده
منابع مشابه
Computing 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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1. Introduction. 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 Demyanenko (see [L3], p. 140) 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 Si...
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If E is a minimal elliptic curve defined over Z, we obtain a bound C, depending only on the global Tamagawa number of E, such that for any point P ∈ E(Q), nP is integral for at most one value of n > C. As a corollary, we show that if E/Q is a fixed elliptic curve, then for all twists E′ of E of sufficient height, and all torsion-free, rank-one subgroups Γ ⊆ E′(Q), Γ contains at most 6 integral ...
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We investigate a problem considered by Zagier and Elkies, of finding large integral points on elliptic curves. By writing down a generic polynomial solution and equating coefficients, we are led to suspect four extremal cases that still might have nondegenerate solutions. Each of these cases gives rise to a polynomial system of equations, the first being solved by Elkies in 1988 using the resul...
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CONTENTS Introduction 1. Elliptic Curves Defined by Simplest Cubic Fields 2. Linear Forms in Elliptic Logarithms 3. Computation of Integral Points 4. Tables of Results 5. General Results about Integral Points on the Elliptic Curves y2 = x3 + mx2 (m+3)x + 1 References Let f(X) be a cubic polynomial defining a simplest cubic field in the sense of Shanks. We study integral points on elliptic curve...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1987
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1987-0866125-3