#### Vol. 1, No. 1, 2013

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Computing equations of curves with many points

### Virgile Ducet and Claus Fieker

Vol. 1 (2013), No. 1, 317–334
##### Abstract

We explain how to compute the equations of the abelian coverings of any curve defined over a finite field. Then we describe an algorithm which computes curves with many rational points with respect to their genus. The implementation of the algorithm provides seven new records over ${\mathbb{F}}_{\mathfrak{2}}$.

##### Keywords
explicit class field theory, Kummer theory, Witt vectors, curves with many points, equations of abelian coverings
Primary: 11R37
Secondary: 14H45
##### Milestones
Published: 14 November 2013
##### Authors
 Virgile Ducet Institut de Mathématiques de Luminy Campus de Luminy, Case 907 13288 Marseille Cedex 9 France Claus Fieker Fachbereich Mathematik Universität Kaiserslautern Postfach 3049 67653 Kaiserslautern Germany