Genus 3 curves whose Jacobians have endomorphisms by Q(ζ7 + ζ-7)

In this work we consider constructions of genus 3 curves X such that End(Jac(X))⊗Q contains the totally real cubic number field Q(ζ7+ζ-7). We construct explicit two-dimensional families defined over Q(s,t) whose generic member is a nonhyperelliptic genus 3 curve with this property. The case when X is hyperelliptic was studied in Hoffman and Wang (2013). We calculate the zeta function of one of these curves. Conjecturally this zeta function is described by a modular form

Genus 3 curves whose jacobians have endomorphisms by Q(ζ7 + ζ7), II

In this work we consider constructions of genus three curves Y such that End(Jac(Y ))⊗Q contains the totally real cubic number field Q(ζ7 + ζ7). We construct explicit three-dimensional families whose general member is a nonhyperelliptic genus 3 curve with this property. The case when Y is hyperelliptic was studied in J. W. HOFFMAN, H. WANG, 7-gons and genus 3 hyperelliptic curves, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales., Serie A. Matemàticas 107 (2013), 35-52, and some nonhyperelliptic curves were constructed in J. W. HOFFMAN, Z. LIANG, Y. SAKAI, H. WANG, Genus 3 curves whose Jacobians have endomorphisms by Q(ζ7 + ζ7), J. Symb. Comp. 74 (2016), 561-577