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manYPoints

manYPoints aims at providing an open access up-to-date source for information on curves over finite fields with many points. It supersedes the earlier website initiated by Gerard van der Geer and Marcel van der Vlugt. It is supported by the Korteweg-de Vries Instituut, Universiteit van Amsterdam.

Submitting improvements

If you think you can contribute an improvement to the tables you are requested to submit it via a form. In order to upload one has to register here. You will be asked for a valid e-mail address, your name and your institute. After confirming your e-mail address you will be able to log in via the form in the upper right corner of this page.

To submit a contribution use the submit form. Your contribution will be reviewed by the moderators before it is added to the database. Do not try to submit any contribution until it is in a final form and you have checked it carefully. Try to be as concise as possible. Your submission can contain a plain text description, a link to an external website or a pdf file. For a new lower bound, please give a short description of the method used. It could be useful to give a description of the curve (if any explicit) and details like the decomposition of its Jacobian, the characteristic polynomial of Frobenius, the automorphism group. A lower bound should satisfy the requirement that it is not less than [b(q,g)/sqrt(2)] with b(q,g) the upper bound for the pair (q,g). For an upper bound, besides a short description of the method(s) used, in case you are dealing with 'defect -1' you could list the zeta functions that are already eliminated.

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There is an RSS feed available here which you can subscribe to in order to always receive the latest updates to the table.

Related and unrelated servers

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Download

Click here to download the entire table. The entries are displayed in the format [q,g,Nmin,Nmax]. Note: in case there is no entry for Nmin (resp. Nmax) then this is replaced by the symbol m (resp. M).

How to cite manYPoints?

The preferred way to cite the manYPoints site (in BibTeX format) is:

AUTHOR = {van der Geer, Gerard and Howe, Everett W. and Lauter, Kristin E. and Ritzenthaler, Christophe}, TITLE = {Tables of Curves with Many Points}, YEAR = {2009}, URL = {http://www.manypoints.org}, NOTE = {Retrieved [insert date here]}

where the author should input the date that the author checked the site. The year 2009 refers to the year that the site was created.

To get BibTex to ignore the "van der" in 'van der Geer' for the purposes of alphabetizing the bibliography, the AUTHOR field should be

AUTHOR = {{\SortNoop{Geer}}van der Geer, Gerard and Howe, Everett W. and Lauter, Kristin E. and Ritzenthaler, Christophe},