TY - MGZN
AU - Cardona, G.
AU - Lario, J.-C.
T2 - Journal of number theory
Y1 - 2020
VL - 2019
SP - 195
EP - 211
DO - 10.1016/j.jnt.2019.08.017
UR - https://www.sciencedirect.com/science/article/pii/S0022314X19302975
AB - Here we study the twists of the genus 2 curve given by the hyperelliptic equation over any field of characteristic different from 2, 3 or 5. Since any curve of genus 2 with group of automorphisms of order 24 is isomorphic (over an algebraically closed field) to the given one, the study of this set of twists is equivalent to the classification, up to isomorphisms defined over the base field, of curves of genus 2 with that number of automorphisms. This contribution closes the series of articles on the classification of twists of curves of genus 2. The knowledge of these twists can be of interest in a wide range of arithmetical questions, such as the Sato-Tate or the Strong Lang conjectures among others.
TI - Twists of the genus 2 curve Y2¿=¿X6¿+¿1
ER -