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$2$ CURVE
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.
