منابع مشابه
Periods of quadratic twists of elliptic curves
In this paper we prove a relation between the period of an elliptic curve and the period of its real and imaginary quadratic twists. This relation is often misstated in the literature.
متن کاملOn the Quadratic Twists of a Family of Elliptic Curves
In this paper, we consider the average size of the 2-Selmer groups of a class of quadratic twists of each elliptic curve over Q with Q-torsion group Z2 × Z2. We prove the existence of a positive proportion of quadratic twists of such a curve, each of which has rank 0 Mordell-Weil group.
متن کاملRanks of Elliptic Curves in Families of Quadratic Twists
In this paper we reformulate the question of whether the ranks of the quadratic twists of an elliptic curve over Q are bounded, into the question of the whether certain infinite series converge. Our results were inspired by ideas in a paper of Gouvêa and Mazur [2]. Fix a, b, c ∈ Z such that f(x) = x + ax + bx+ c has 3 distinct complex roots, and let E be the elliptic curve y = f(x). For D ∈ Z−{...
متن کاملSelmer Groups of Quadratic Twists of Elliptic Curves
(1.1) E : y + a1xy + a3y = x + a2x + a4x+ a6 where a1, a2, a3, a4, a6 ∈ Z. Let N(E) denote the conductor of E, j(E) the j-invariant of E, and L(E, s) = ∑∞ n=1 a(n)n −s the Hasse-Weil L-function of E. If E is modular, then let FE(z) = ∑∞ n=1 aE(n)q n ∈ S2(N(E), χ1) be the associated weight 2 cusp form. Here χ1 denotes the trivial Dirichlet character. Throughout, D will denote a square-free integ...
متن کامل2-selmer Groups of Quadratic Twists of Elliptic Curves
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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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2014
ISSN: 0024-6115
DOI: 10.1112/plms/pdu059