FAMILY OF ELLIPTIC CURVES <em>E<sup></em>(<em>p</em>,<em>q</em>)</sup>: <em>y</em><sup>2</sup>=<em>x</em><sup>2</sup>-<em>p</em><sup>2</sup><em>x</em>+<em>q</em><sup>2</sup>
نویسندگان
چکیده
منابع مشابه
On Silverman's conjecture for a family of elliptic curves
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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Let E=Q(T) be a one-parameter family of elliptic curves. Assuming various standard conjectures, we give an upper bound for the average rank of the bers E t (Q) with t 2 Z, improving earlier estimates of Fouvry-Pomykala and Michel. We also show how certain assumptions about the distribution of zeros of L-series might help explain the experimentally observed fact that the average rank of the bers...
متن کاملon silverman's conjecture for a family of elliptic curves
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: Facta Universitatis, Series: Mathematics and Informatics
سال: 2019
ISSN: 2406-047X,0352-9665
DOI: 10.22190/fumi1904805k