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.
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Publisher's URL: http://www.ams.org/journals/mcom/1994-62-205/S0025-5718-1994-1185241-6/
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 |
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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 |
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