Abstract
Let E and A be elliptic curves over a number field K. Letχ be a quadratic character of K. We prove the conjecture posed by Mazur and Rubin on n-Selmer near-companion curves in the case n = 2. Namely, we show if the difference of the 2-Selmer ranks of Eχ and Aχ is bounded independent of χ, there is a GK -module isomorphism E[2] (Formula Persented) A[2].
Original language | English |
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Pages (from-to) | 425-440 |
Number of pages | 16 |
Journal | Transactions of the American Mathematical Society |
Volume | 372 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2019 |
Bibliographical note
Publisher Copyright:© 2018 American Mathematical Society.
All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics