We construct a three-parameter family of nonhyperelliptic and bielliptic plane genus-three curves whose associated Prym variety is two-isogenous to the Jacobian variety of a general hyperelliptic genus-two curve. Our construction is based on the existence of special elliptic fibrations with the section on the associated Kummer surfaces that provide a simple geometric interpretation for the rational double cover induced by the two-isogeny between the Abelian surfaces.
"On Isogenies Among Certain Abelian Surfaces." Michigan Math. J. Advance Publication 1 - 43, 2021. https://doi.org/10.1307/mmj/20195790