Torsion groups of a family of elliptic curves over number fields
We compute the torsion group explicitly over quadratic fields and number fields of degree coprime to 6 for a family of elliptic curves of the form , where is an integer.
We compute the torsion group explicitly over quadratic fields and number fields of degree coprime to 6 for a family of elliptic curves of the form , where is an integer.
Let be an algebraic family of Drinfeld modules defined over a field K of characteristic p, and let a,b ∈ K[λ]. Assume that neither a(λ) nor b(λ) is a torsion point for for all λ. If there exist infinitely many λ ∈ K̅ such that both a(λ) and b(λ) are torsion points for , then we show that for each λ ∈ K̅, a(λ) is torsion for if and only if b(λ) is torsion for . In the case a,b ∈ K, we prove in addition that a and b must be -linearly dependent.