Doubly isogenous curves of genus two with a rational action of $D_6$

Jeremy Booher, Everett W. Howe, Andrew V. Sutherland +1

Let $C$ and $C^{\prime }$ be curves over a finite field $K$, provided with embeddings ${\hat{I}}^1$ and $ι'$ into their Jacobian varieties. Let $D\to C$ and $D^{\prime }\to C^{\prime }$ be the pullbacks (via these e…