Key points are not available for this paper at this time.
In this paper, we introduce the study of minimal torsion curves within a fixed geometric isogeny class. For a Q-isogeny class E of elliptic curves and N Z^+, we wish to determine the least degree of a point on the modular curve X₁ (N) associated to any E E. In the present work, we consider the cases where E is rational, i. e. , contains an elliptic curve with rational j-invariant, or where E consists of elliptic curves with complex multiplication (CM). If N=ᵏ is a power of a single prime, we give a complete characterization upon restricting to points of odd degree, and also in the case where E is CM. We include various partial results in the more general setting.
Bourdon et al. (Fri,) studied this question.