Counting points on geometrically hyperelliptic curves of genus three
Talk by Dr. Maike Massierer
Date: 09.09.16 Time: 15.00 - 16.00 Room:
Let C/Q be a curve of genus 3, given as a double cover of a plane conic. Such a curve is hyperelliptic over the algebraic closure of Q, but may not have a hyperelliptic model of the usual form over Q. For a prime p of good reduction, let C_p be the reduction of C modulo p. We discuss an algorithm that counts points on the curves C_p simultaneously at all good p up to a prescribed bound N. We briefly report on our implementation, and compare its performance to previous algorithms for the ordinary hyperelliptic case.Joint work with David Harvey and Andrew V. Sutherland.