DECOMPOSITION OF THE JACOBIAN OF SOME TWISTS OF A GENUS 2 CURVE

Abstract

Cardona and Lario ['Twists of the genus 2 curve y(2) = x(6)+1 ', J. Number Theory 209 (2020), 195-211] gave a complete classification of the twists of the curve y(2) = x(6)+1 . In this paper, we study the twists of the curve whose automorphism group is defined over a biquadratic extension of the rationals. If the twists are of type B or C in the Cardona-Lario classification, we find a pair of elliptic curves whose product is isogenous with the Jacobian of the twist.