Currently available as a preprint.

We study the zeta functions of curves over finite fields. Suppose *C*_{1} and *C*_{2}
are curves over a finite field *K*, with *K*-rational base points *P*_{1} and *P*_{2},
and let *D*_{1} and *D*_{2} be the pullbacks (via the Abel–Jacobi map) of the
multiplication-by-2 maps on their Jacobians. We say that (*C*_{1}, *P*_{1}) and (*C*_{1}, *P*_{2})
are *doubly isogenous* if Jac(*C _{1}*) and Jac(

We used Magma to gather data and to test our heuristics. The code we used, and the data it produced for doubly-isogenous curves, is available here: