Computational aspects of curves of genus at least 2.(English)Zbl 0891.11037

Cohen, Henri (ed.), Algorithmic number theory. Second international symposium, ANTS-II, Talence, France, May 18-23, 1996. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1122, 283-306 (1996).
This paper gives an impressive and accessible account of computational results and methods for curves of genus greater than one. The author gives discussions on various topics including computing in the Jacobian of such curves, computing the number of points on the curve and its Jacobian over finite fields, computation of the Mordell-Weil group of the Jacobian. The author then goes on to discuss work in the construction of curves with various properties such as a large number of rational points, a rational torsion point of large order or given bad reduction. The paper ends with some examples, open problems and an extensive bibliography.
For the entire collection see [Zbl 0852.00023].

MSC:

 11G30 Curves of arbitrary genus or genus $$\ne 1$$ over global fields 14Q05 Computational aspects of algebraic curves