Constructing one-parameter families of elliptic curves with moderate rank

JOURNAL OF NUMBER THEORY

卷:123

Article

Arms, Scott ; Lozano-Robledo, Alvaro ; Miller, Steven J.

关键词: elliptic curves;    rational elliptic surfaces;    Mordell-Weil rank;   

DOI  :  10.1016/j.jnt.2006.07.002

来源: Elsevier

【 摘 要 】

We give several new constructions for moderate rank elliptic curves over Q(T). In particular we construct infinitely many rational elliptic surfaces (not in Weierstrass form) of rank 6 over Q using polynomials of degree two in T. While our method generates linearly independent points, we are able to show the rank is exactly 6 without having to verify the points are independent. The method generalizes; however, the higher rank surfaces are not rational, and we need to check that the constructed points are linearly independent. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free