Twists of Elliptic curves over function fields with a large set of integral points

Details Twists of Elliptic curves over function fields with a large set of integral points Twists of Elliptic curves over function fields with a large set of integral points

2009-10-18

arxiv.org/abs/0910.3417v1

Mathematics

Number Theory

24 pages

Scientific paper

For $q\equiv 3 \mod 4$, we show that there are quadratic twists of supersingular elliptic curves with an arbitrarily large set of separable $\infty - $integral points over $\ff_q(t)$. We also show that the same holds true if we consider cubic twists of $y^2=x^3+1$ in the supersingular case, i.e, $q\equiv 2\mod 3$. These examples allow us to show that the conjecture of Lang-Vojta concerning the behavior of integral points in varieties of log-general type cannot be readily transported to the function field case. Also for $q\equiv 2 \mod 3$ and $q\equiv 3\mod 4$ they provide examples of elliptic curves over $\ff_q(t)$ with an explicit set of linearly independent points with an arbitrarily large size. Finally, we will use them to construct quadratic and cubic function fields with arbitrarily large $m$-class rank, for $m$ dividing $q+1$.

Affiliated with

Also associated with

No associations

Rating

Twists of Elliptic curves over function fields with a large set of integral points 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 Twists of Elliptic curves over function fields with a large set of integral points, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Twists of Elliptic curves over function fields with a large set of integral points will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-715936