Torsion points on y^2=x^6+1

Details Torsion points on y^2=x^6+1 Torsion points on y^2=x^6+1

1997-10-20

arxiv.org/abs/math/9710224v1

Mathematics

Number Theory

Scientific paper

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.

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