Elementary 3-descent with a 3-isogeny

Abstract

In this expository paper, we show how to use in practice 3-descent with a 3-isogeny to find an estimate for the rank of an elliptic curve having a rational 3-torsion subgroup, and we also give a geometric interpretation of these computations.

References in corpus (1)

• Parity of ranks for elliptic curves with a cyclic isogeny

Cited by in corpus (9)

• Second Isogeny Descents and the Birch and Swinnerton-Dyer Conjectural Formula
• Three-isogeny Selmer groups and ranks of abelian varieties in quadratic twist families over a number field
• Two and three descent for elliptic curves associated with perfect cuboids
• Descent on elliptic curves
• Quadratic Twists of Elliptic Curves with 3-Selmer Rank 1
• A parametrized set of explicit elements of $\Sha(E/\Q)[3]$
• Infinitely many elliptic curves of rank exactly two, II
• The $3$-isogeny Selmer groups of the elliptic curves $y^2=x^3+n^2$
• On parameterizations of cyclic $N$-isogenies and strict $K$-curves lying above rational points of $Y_0^{+}(N)$