Title

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

Document Type

Article

Publication Date

1-1-2016

Abstract

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.

Publication Source (Journal or Book title)

Journal of Symbolic Computation

First Page

561

Last Page

577

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