Descent by 3-isogeny and 3-rank of quadratic fields
Jaap Top · 1993
Abstract In this paper families of elliptic curves admitting a rational isogeny of degree 3 are studied. It is known that the 3-torsion in the class group of the field defined by the points in the kernel of such an isogeny is related to the rank of the elliptic curve. Families in which almost all the curves have rank at least 3 are constructed. In some cases this provides lower bounds for the number of quadratic fields which have a class number divisible by 3.