Maximal ranks and integer points on a family of elliptic curves
نویسندگان
چکیده
منابع مشابه
Maximal Ranks and Integer Points on a Family of Elliptic Curves
We extend a result of Spearman which provides a sufficient condition for elliptic curves of the form y2 = x3 − px, with p a prime, to have Mordell-Weil rank 2. As in Spearman’s work, the condition given here involves the existence of integer points on these curves.
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Let $E$ be an elliptic curve over $Bbb{Q}$ with the given Weierstrass equation $ y^2=x^3+ax+b$. If $D$ is a squarefree integer, then let $E^{(D)}$ denote the $D$-quadratic twist of $E$ that is given by $E^{(D)}: y^2=x^3+aD^2x+bD^3$. Let $E^{(D)}(Bbb{Q})$ be the group of $Bbb{Q}$-rational points of $E^{(D)}$. It is conjectured by J. Silverman that there are infinitely many primes $p$ for which $...
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ژورنال
عنوان ژورنال: Glasnik Matematicki
سال: 2009
ISSN: 0017-095X
DOI: 10.3336/gm.44.1.04