Average size of $2$-Selmer groups of elliptic curves, I
نویسندگان
چکیده
منابع مشابه
Average Size of 2-selmer Groups of Elliptic Curves, I
In this paper, we study a class of elliptic curves over Q with Qtorsion group Z2×Z2, and prove that the average order of the 2-Selmer groups is bounded.
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In this paper, we consider the average order of the 2-Selmer groups of elliptic curves over Q given by the equation E : y2 = x(x + a)(x + b), where a and b are integers. We show that, with a being fixed, the average order of the 2-Selmer groups of such curves closely depends on a. More exactly, we show that the average order is bounded if |a| is not a square and unbounded if |a| is the square o...
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Employing a geometric setting inspired by the proof of the Fundamental Lemma, we study some counting problems related to the average size of 2-Selmer groups and hence obtain an estimate for it.
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In this paper we investigate families of quadratic twists of elliptic curves. Addressing a speculation of Ono, we identify a large class of elliptic curves for which the parities of the “algebraic parts” of the central values L(E/Q, 1), as d varies, have essentially the same multiplicative structure as the coefficients ad of L(E/Q, s). We achieve this by controlling the 2-Selmer rank (à la Mazu...
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Let E : y = F (x) be an elliptic curve over Q defined by a monic irreducible integral cubic polynomial F (x) with negative and square-free discriminant −D. We determine its 2-Selmer rank in terms of the 2-rank of the class group of the cubic field L = Q[x]/F (x). We then interpret this result as a mod 2 congruence between the Hasse-Weil L-function of E and a degree two Artin L-function associat...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2005
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-05-03806-7