  Let C/Q be a curve of genus three, given as a double cover of a plane conic.
Such a curve is hyperelliptic over the algebraic closure of Q, but may not have
a hyperelliptic model of the usual form over Q. We describe an algorithm that
computes the local zeta functions of C at all odd primes of good reduction up
to a prescribed bound N. The algorithm relies on an adaptation of the
"accumulating remainder tree" to matrices with entries in a quadratic field. We
report on an implementation, and compare its performance to previous algorithms
for the ordinary hyperelliptic case.
