Elementary 3-descent with a 3-isogeny

Henri Cohen (1, 2) , Fabien Pazuki (1, 3)

1 IMB - Institut de Mathématiques de Bordeaux
2 LFANT - Lithe and fast algorithmic number theory
3 UB - Université Sciences et Technologies - Bordeaux 1

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.

Domaines: Théorie des nombres [math.NT]

Henri Cohen, Fabien Pazuki. Elementary 3-descent with a 3-isogeny. Acta Arithmetica, 2009, 140 (4), pp.369-404. ⟨hal-00778445⟩