Computing the rank of elliptic curves over real quadratic number fields of class number 1
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- by J. E. Cremona and P. Serf PDF
- Math. Comp. 68 (1999), 1187-1200 Request permission
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.References
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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.
- MR Author ID: 52705
- ORCID: 0000-0002-7212-0162
- 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
- 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 513 009 738 3.
- © Copyright 1999 American Mathematical Society
- Journal: Math. Comp. 68 (1999), 1187-1200
- MSC (1991): Primary 11G05, 11Y16, 11Y50, 14G25, 14H52, 14Q05
- DOI: https://doi.org/10.1090/S0025-5718-99-01055-8
- MathSciNet review: 1627777