Some families of Mordell curves associated to cubic fields

[摘要] We introduce some Mordell curves of two different natures both of which are associated to cubic fields. One set of them consists of those elliptic curves whose rational points over the rational number field are described by or closely related to cubic fields. The other is a one-parameter family of Mordell curves which gives all (cyclic) cubic twists and all quadratic twists of the Fermat curve X-3 + Y-3 + Z(3) = 0. (C) 2003 Elsevier B.V. All rights reserved.

[发布日期] 2003-11-01

[效力级别]  Proceedings Paper

[关键词] Mordell curves;cubic fields