On the rank of certain parametrized elliptic curves

Details On the rank of certain parametrized elliptic curves On the rank of certain parametrized elliptic curves

2012-01-27

arxiv.org/abs/1201.5731v1

Mathematics

Number Theory

Scientific paper

In this paper the family of elliptic curves over \Q given by the equation E_{p}: Y^2=(X-p)^3+X^3+(X+p)^3 where p is a prime number, is studied. It is shown that the maximal rank of the elliptic curves is at most 3 and some conditions under which we have rank(E_p(\Q))=0 or rank(E_p(\Q))=1 or rank(E_p(\Q))>=2 are given. Moreover It is shown that in the family there are elliptic curves with rank 0,1,2 and 3.

Affiliated with

Also associated with

No associations

Rating

On the rank of certain parametrized elliptic curves 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 On the rank of certain parametrized elliptic curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the rank of certain parametrized elliptic curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-344536