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In this work we consider constructions of genus three curves $X$ such that$\mathrm{End}(\mathrm{Jac} (X))\otimes Q$ contains the totally real cubicnumber field $Q(\zeta _7 +\bar{\zeta}_7 )$. We construct explicitthree-dimensional families whose generic member is a nonhyperelliptic genus 3curve with this property. The case when $X$ is hyperelliptic was studied in aprevious work by Hoffman and Wang and some nonhyperelliptic curves wereconstructed in a previous paper by Hoffman, Z. Liang. Sakai and Wang.

Genus 3 curves whose Jacobians have endomorphisms by $Q (\zeta _7 +\bar{\zeta}_7 )$, II