Selmer groups of families of elliptic curves with an ℓ-isogeny

2025/08/29 by Chan, Stephanie, Verzobio, Matteo · 1 citation
#11G05 (11N36) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.21406

Abstract

For certain families of elliptic curves admitting a rational isogeny of prime degree ℓ, we establish a central limit theorem for the Tamagawa ratio and derive bounds on its average value. By using the Tamagawa ratio to bound the size of the ℓ-isogeny Selmer group from below, we show that for ℓ ∈\ 2, 3, 5, 7, 13\, there exist elliptic curves with arbitrarily large ℓ-Selmer groups.

Citations

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Cited by

• Unbounded average Selmer ranks of elliptic curves in torsion families

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