Title:
Prime torsion order on elliptic curves over number fields of small
degree
Abstract:
This is joint work with Maarten Derickx, Sheldon Kamienny and William
Stein.
For a positive integer d, we define S(d) to be the set of all prime
numbers that occur as the order of a K-rational torsion point on an
elliptic curve over a number field K of degree d. Prior to our work,
the following sets S(d) were known:
S(1) = {2, 3, 5, 7} (Mazur)
S(2) = {2, 3, 5, 7, 11, 13} (Kamienny)
S(3) = {2, 3, 5, 7, 11, 13} (Parent)
We determine S(4), S(5) and S(6), and come close to determining S(7).