Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Genus 3 curves whose Jacobians have endomorphisms by $Q(\zeta _7 +
  \overline{\zeta}_7)$   In this work we consider constructions of genus three curves $X$ such that
$\mathrm{End}(\mathrm{Jac}(X)) \otimes Q$ contains the totally real cubic
number field $Q(\zeta _ 7 + \overline{\zeta}_7)$. 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 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.

16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat