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

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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.

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Tokyo Journal of Mathematics

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