Selmer groups of twists of elliptic curves over K with K-rational torsion points

摘要

We generalize a result of Frey on Selmer groups of twists of elliptic curves over $$mathbf Q $$ Q with $$mathbf Q $$ Q -rational torsion points to elliptic curves defined over number fields of small degree K with a K -rational torsion point. We also provide examples of elliptic curves coming from Zywina that satisfy the conditions of our Corollary D.