Computing equations of curves with many points

Virgile Ducet (1) , Claus Fieker (2)

1 IML - Institut de mathématiques de Luminy
2 TU Kaiserslautern - Technische Universität Kaiserslautern

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 7 new records over F 2 .

Domaines: Théorie des nombres [math.NT]

Virgile Ducet, Claus Fieker. Computing equations of curves with many points. Everett W. Howe and Kiran S. Kedlaya. Proceedings of the Tenth Algorithmic Number Theory Symposium, 1 (1), Math. Sci. Publ., Berkeley, CA, pp.317--334, 2013, The Open Book Series, 978-1-935107-00-2. ⟨10.2140/obs.2013.1.317⟩. ⟨hal-01309420⟩