Periods of cusp forms and elliptic curves over imaginary quadratic number fields

Cremona, J.E. and Whitley, E. (1994) Periods of cusp forms and elliptic curves over imaginary quadratic number fields. Mathematics of Computation, 62, pp. 407-429.

Abstract

In this paper we explore the arithmetic correspondence between, on the one hand, (isogeny classes of) elliptic curves E defined over an imaginary quadratic field K of class number one, and on the other hand, rational newforms F of weight two for the congruence subgroups , where n is an ideal in the ring of integers R of K. This continues work of the first author and forms part of the Ph.D. thesis of the second author. In each case we compute numerically the value of the L-series at and compare with the value of which is predicted by the Birch-Swinnerton-Dyer conjecture, finding agreement to several decimal places. In particular, we find that whenever has a point of infinite order. Several examples are given in detail from the extensive tables computed by the authors.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Whitley, Dr Elise
• Authors: Cremona, J.E., and Whitley, E.
• College/School: College of Medical Veterinary and Life Sciences > School of Health & Wellbeing > MRC/CSO SPHSU
• Journal Name: Mathematics of Computation
• ISSN: 0025-5718
• ISSN (Online): 1088-6842