The average size of the 3‐isogeny Selmer groups of elliptic curves y2=x3+k

DOI10.1112/jlms.12271zbMath1458.11091arXiv1610.05759OpenAlexW2539140476MaRDI QIDQ5108151

Ari Shnidman, Manjul Bhargava, Noam D. Elkies

Publication date: 29 April 2020

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.05759

zbMATH Keywords

average rankelliptic curves over number fieldsdensity of low rank elliptic curves

Mathematics Subject Classification ID

Forms of degree higher than two (11E76) Elliptic curves over global fields (11G05) Density theorems (11R45)

Related Items (9)

Elements of prime order in Tate–Shafarevich groups of abelian varieties over ⋮ Arithmetic statistics of Prym surfaces ⋮ Rank growth of elliptic curves over 𝑁-th root extensions ⋮ Analytic number theory. Abstracts from the workshop held November 6--12, 2022 ⋮ Cube sum problem for integers having exactly two distinct prime factors ⋮ MANY CUBIC SURFACES CONTAIN RATIONAL POINTS ⋮ GOLDFELD’S CONJECTURE AND CONGRUENCES BETWEEN HEEGNER POINTS ⋮ Elements of given order in Tate-Shafarevich groups of abelian varieties in quadratic twist families ⋮ \(3\)-isogeny Selmer groups and ranks of abelian varieties in quadratic twist families over a number field

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