In many families of elliptic curves with a rational prime-degree isogeny, the logarithmic Tamagawa ratio satisfies a central limit theorem, yielding curves with arbitrarily large ℓ-Selmer groups for ℓ = 2, 3, 5, 7, 13.
Serre.Lectures onNX (p), volume 11 ofChapman & Hall/CRC Research Notes in Mathematics
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Selmer groups of families of elliptic curves with an $\ell$-isogeny
In many families of elliptic curves with a rational prime-degree isogeny, the logarithmic Tamagawa ratio satisfies a central limit theorem, yielding curves with arbitrarily large ℓ-Selmer groups for ℓ = 2, 3, 5, 7, 13.