Skip to main content

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
Cancel
×
Home
Article
    • Aa
    • Aa
  • Cited by 4
  • Cited by
    Crossref Citations
    Crossref logo
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    MacLeod, Allan 2015. On two of John Leech's unsolved problems concerning Rational cuboids. Glasnik Matematicki, Vol. 50, Issue. 2, p. 269.

    Yokoyama, Shun’ichi 2012. On Elliptic Curves with Everywhere Good Reduction over Certain Number Fields. American Journal of Computational Mathematics, Vol. 02, Issue. 04, p. 358.

    Cremona, J.E. and Fisher, T.A. 2009. On the equivalence of binary quartics. Journal of Symbolic Computation, Vol. 44, Issue. 6, p. 673.

    O’Neil, Catherine 2005. Models of some genus one curves with applications to descent. Journal of Number Theory, Vol. 112, Issue. 2, p. 369.

    ×
  • Access

Computing the Rank of Elliptic Curves over Number Fields

  • Denis Simon (a1)
Abstract
Abstract

This paper describes an algorithm of 2-descent for computing the rank of an elliptic curve without 2-torsion, defined over a general number field. This allows one, in practice, to deal with fields of degree from 1 to 5.

    •
      • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Computing the Rank of Elliptic Curves over Number Fields
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      Computing the Rank of Elliptic Curves over Number Fields
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      Computing the Rank of Elliptic Curves over Number Fields
      Available formats
      ×
Copyright
COPYRIGHT: © London Mathematical Society 2002
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

6 H. Cohen , Advanced topics in computational algebraic number theory, Grad. Texts in Math. 193 (Springer, 2000).
9 J. E. Cremona , ‘Classical invariants and 2-descent on elliptic curves’, J. Symb. Comput. 31 (2001) 71–87.
10 J. E. Cremona , D. Rusin , ‘Efficient solution of rational conics’, Math. Comp. (2002), to appear.
11 J. E. Cremona , P. Serf , ‘Computing the rank of elliptic curves over real quadratic fields of class number 1‘, Math.Comp. 68 (1999) 1187–1200.
12 J. E. Cremona and E. Whitley , ‘Periods of cusp forms and elliptic curves over imaginary quadratic fields’, Math.Comp. 62 (1994) 407–429.
14 Z. Djabri , E. F. Schaefer and N. P. Smart , ‘Computing the P-Selmer group of an elliptic curve’, Trans. Amer. Math. Soc. 352 (2000) 5583–5597.
15 S. Lang , Algebraic number theory, Grad. Texts in Math. 110, 2nd edn (Springer,1994).
18 E. F. Schaefer , ‘2-descent on the Jacobians of hyperelliptic curves’, J.Number Theory 51 (1995) 219–232.
19 E. F. Schaefer , ‘Class groups and Selmer groups‘, J.Number Theory 56 (1996) 79–114.
22 D. Simon , ‘Solving norm equations using S-units’, Math.Comp. (2002), to appear.
25 M. Stoll , ‘Implementing 2-descent for Jacobians of elliptic curves’, Acta Arith. 98 (2001) 245–277.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

LMS Journal of Computation and Mathematics
  • ISSN: -
  • EISSN: 1461-1570
  • URL: /core/journals/lms-journal-of-computation-and-mathematics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

CAPTCHA *

Skip to the audio challenge
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 100 *
Loading metrics...

Abstract views

Total abstract views: 41 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 23rd May 2017. This data will be updated every 24 hours.

Cancel
Confirm
×