Mathematics – Number Theory
Scientific paper
2011-03-30
Mathematics
Number Theory
19 pages
Scientific paper
We describe methods to determine all the possible torsion groups of an elliptic curve that actually appear over a fixed quadratic field. We use these methods to find, for each group that can appear over a quadratic field, the field with the smallest absolute value of it's discriminant such that there exists an elliptic curve with that torsion. We also examine the interplay of the torsion and rank over a fixed quadratic field and see that what happens is very different than over $\Q$. Finally we give some results concerning the number and density of fields with an elliptic curve with given torsion over them.
Kamienny Sheldon
Najman Filip
No associations
LandOfFree
Torsion groups of elliptic curves over quadratic 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 Torsion groups of elliptic curves over quadratic fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Torsion groups of elliptic curves over quadratic fields will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-568513