Genus 3 curves whose Jacobians have endomorphisms by $Q(\zeta _7 + \overline{\zeta}_7)$
Algebraic Geometry
2014-11-11 v1
Abstract
In this work we consider constructions of genus three curves such that contains the totally real cubic number field . We construct explicit two-dimensional families defined over whose generic member is a nonhyperelliptic genus 3 curve with this property. The case when X is hyperelliptic was studied by the authors Hoffman and Wang in a previous work. We calculate the zeta function of one of these curves. Conjecturally this zeta function is described by a modular form.
Keywords
Cite
@article{arxiv.1411.2151,
title = {Genus 3 curves whose Jacobians have endomorphisms by $Q(\zeta _7 + \overline{\zeta}_7)$},
author = {J. William Hoffman and Zhibin Liang and Yukiko Sakai and Haohao Wang},
journal= {arXiv preprint arXiv:1411.2151},
year = {2014}
}