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math.NT2011★ 13 cited
Second Isogeny Descents and the Birch and Swinnerton-Dyer Conjectural Formula
Brendan Creutz, Robert L. Miller
Let h be a p-isogeny of elliptic curves. We describe how to perform h-descents on the nontrivial elements in the Shafarevich-Tate group which are killed by the dual isogeny h'. Thi…
math.NT2010★ 1 cited
Explicit isogeny descent on elliptic curves
R. L. Miller, M. Stoll
In this note, we consider an l-isogeny descent on a pair of elliptic curves over Q. We assume that l > 3 is a prime. The main result expresses the relevant Selmer groups as kernels…
math.NT2010★ 2 cited
Proving the Birch and Swinnerton-Dyer conjecture for specific elliptic curves of analytic rank zero and one
R. L. Miller
We describe an algorithm to prove the Birch and Swinnerton-Dyer conjectural formula for any given elliptic curve defined over the rational numbers of analytic rank zero or one. Wit…