Torsion points on y^2=x^6+1
Number Theory
2007-05-23 v1
Abstract
Let C be the curve y^2=x^6+1 of genus 2 over a field of characteristic zero. Consider C embedded in its Jacobian J by sending one of the points at infinity on C to the origin of J. In this brief note we show that the points of C whose image on J are torsion are precisely the two points at infinity and the six points with y=0.
Keywords
Cite
@article{arxiv.math/9710224,
title = {Torsion points on y^2=x^6+1},
author = {José Felipe Voloch},
journal= {arXiv preprint arXiv:math/9710224},
year = {2007}
}