Constructing families of 3-Selmer companions
Abstract
Mazur and Rubin introduced the notion of n-Selmer companion elliptic curves and gave several examples of pairs of non-isogenous Selmer companions. We construct several pairs of families of elliptic curves, each parameterised by t∈, such that the two curves in a pair corresponding to a given t are non-isogenous 3-Selmer companions, possibly provided that t satisfies a simple congruence condition.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.