Genus 3 curves whose Jacobians have endomorphisms by Q (ζ₇ +ζ₇), II
Hoffman, J. W. · Liang, Dun · Liang, Zhibin · Okazaki, Ryotaro · Sakai, Yukiko · Wang, Haohao
Original · EN
In this work we consider constructions of genus three curves X such that End(Jac (X))⊗ Q contains the totally real cubic number field Q(ζ₇ +ζ₇). We construct explicit three-dimensional families whose generic member is a nonhyperelliptic genus 3 curve with this property. The case when X is hyperelliptic was studied in a previous work by Hoffman and Wang and some nonhyperelliptic curves were constructed in a previous paper by Hoffman, Z. Liang. Sakai and Wang.
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