Complete classification of torsion of elliptic curves over quadratic cyclotomic fields

Details Complete classification of torsion of elliptic curves over quadratic cyclotomic fields Complete classification of torsion of elliptic curves over quadratic cyclotomic fields

2010-05-04

arxiv.org/abs/1005.0560v1

J. Number Theory 130 (2010), 1964-1968

Mathematics

Number Theory

6 pages, to appear in J. Number Theory

Scientific paper

In a previous paper, the author examined the possible torsions of an elliptic curve over the quadratic fields $\mathbb Q(i)$ and $\mathbb Q(\sqrt{-3})$. Although all the possible torsions were found if the elliptic curve has rational coefficients, we were unable to eliminate some possibilities for the torsion if the elliptic curve has coefficients that are not rational. In this note, by finding all the points of two hyperelliptic curves over $\mathbb Q(i)$ and $\mathbb Q(\sqrt{-3})$, we solve this problem completely and thus obtain a classification of all possible torsions of elliptic curves over $\mathbb Q(i)$ and $\mathbb Q(\sqrt{-3})$.

Affiliated with

Also associated with

No associations

Rating

Complete classification of torsion of elliptic curves over quadratic cyclotomic fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Complete classification of torsion of elliptic curves over quadratic cyclotomic fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Complete classification of torsion of elliptic curves over quadratic cyclotomic fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-532370