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Strong Selmer Companion Elliptic Curves
- Chiu, Ching-Heng
- Advisor(s): Rubin, Karl C
Abstract
Let $E_1$ and $E_2$ be elliptic curves defined over a number field $K$. Suppose that for all but finitely many primes $\ell$, and for all finite extension fields $L/K$,
$$\dim_{\mathbb{F}_\ell}\mathrm{Sel}_{\ell}(L,E_1)=\dim_{\mathbb{F}_\ell}\mathrm{Sel}_{\ell}(L,E_2).$$ We prove that $E_1$ and $E_2$ are isogenous over $K$.
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