Computing the rank of elliptic curves over real quadratic number fields of class number 1-Reference-Cited by-同舟云学术

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

Published:1999-02-15 Issue:227 Volume:68 Page:1187-1200
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Cremona J.,Serf P.

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 Q \mathbb {Q} . Several examples are included.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1999-68-227/S0025-5718-99-01055-8/S0025-5718-99-01055-8.pdf

Reference11 articles.

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2. J. E. Cremona, Algorithms for Modular Elliptic Curves (Second Edition), Cambridge University Press, 1997.

3. J. E. Cremona, Classical invariants and elliptic curves, preprint, 1996.

4. The Wadsworth \& Brooks/Cole Mathematics Series;Garrett, Paul B.,1990

5. H. Graf, Konstruktion elliptischer Kurven hohen Ranges über quadratischen Zahlkörpern der Klassenzahl eins, Diploma thesis, Universität des Saarlandes, Saarbrücken, 1995.

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