2-selmer Groups and the Birch-swinnerton-dyer Conjecture for the Congruent Number Curves
نویسنده
چکیده
We take an approach toward counting the number of n for which the curve En : y = x3−n2x has 2-Selmer groups of a given size. This question was also discussed in a pair of papers by Roger Heath-Brown [6, 7]. We discuss the connection between computing the size of these Selmer groups and verifying cases of the Birch and Swinnerton-Dyer Conjecture. The key ingredient for the asymptotic formulae is the “independence” of the Legendre symbol evaluated at the prime divisors of an integer with exactly k prime factors.
منابع مشابه
On the elliptic curves of the form $ y^2=x^3-3px $
By the Mordell-Weil theorem, the group of rational points on an elliptic curve over a number field is a finitely generated abelian group. There is no known algorithm for finding the rank of this group. This paper computes the rank of the family $ E_p:y^2=x^3-3px $ of elliptic curves, where p is a prime.
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