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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Computing the rank of elliptic curves
over real quadratic number fields
of class number 1


Authors: J. E. Cremona and P. Serf
Journal: Math. Comp. 68 (1999), 1187-1200
MSC (1991): Primary 11G05, 11Y16, 11Y50, 14G25, 14H52, 14Q05
Published electronically: February 15, 1999
MathSciNet review: 1627777
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we describe an algorithm for computing the rank of an elliptic curve defined over a real quadratic field of class number one. This algorithm extends the one originally described by Birch and Swinnerton-Dyer for curves over $\mathbb{Q}$. Several examples are included.


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Additional Information

J. E. Cremona
Affiliation: Department of Mathematics, University of Exeter, Laver Building, North Park Road, Exeter EX4 4QE, U.K.
Email: cremona@maths.exeter.ac.uk

P. Serf
Affiliation: Fachbereich 9 Mathematik, Universität des Saarlandes, Postfach 151150, D-66041 Saarbrücken, Germany
Email: pascale@math.uni-sb.de

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01055-8
PII: S 0025-5718(99)01055-8
Keywords: Elliptic curves, Mordell-Weil, real quadratic fields
Received by editor(s): June 7, 1996
Received by editor(s) in revised form: January 22, 1998
Published electronically: February 15, 1999
Additional Notes: The second author was supported in part by DFG grant 5130097383.
Article copyright: © Copyright 1999 American Mathematical Society