Hyperelliptic curves covering an elliptic curve twice
Algebraic Geometry
2013-03-19 v1 Number Theory
Abstract
We show that for any elliptic curve (with j invariant not 0 or 1728) over any field of characteristic different from 2 and 3, there exists an hyperelliptic curve H of genus 5 with two independent maps to the given elliptic curve. We also show that, if we want such a curve to be just geometrically hyperelliptic, so having a degree two map to a conic, then there are some with genus 3.
Keywords
Cite
@article{arxiv.1303.4220,
title = {Hyperelliptic curves covering an elliptic curve twice},
author = {Xavier Xarles},
journal= {arXiv preprint arXiv:1303.4220},
year = {2013}
}
Comments
3 pages