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 (Formula Persented) A.
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© 2018 American Mathematical Society.
All Science Journal Classification (ASJC) codes
- Applied Mathematics