On 2-Selmer groups and quadratic twists of elliptic curves

被引：0

作者：

Salazar, Daniel Barrera ^{[1
]}

Pacetti, Ariel ^{[2
]}

Tornaria, Gonazalo ^{[3
]}

机构：

[1] Univ Santiago Chile, DMCC, Alameda, Santiago 3363, Chile

[2] Univ Aveiro, Ctr Res & Dev Math & Applicat CIDMA, Dept Math, P-3810193 Aveiro, Portugal

[3] Univ Republica, Igua 4225 Esquina Mataojo, Montevideo 11400, Uruguay

来源：

MATHEMATICAL RESEARCH LETTERS | 2021年 / 28卷 / 06期

关键词：

CONDUCTOR;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let K be a number field and E/K be an elliptic curve with no 2-torsion points. In the present article we give lower and upper bounds for the 2-Selmer rank of E in terms of the 2-torsion of a narrow class group of a certain cubic extension of K attached to E. As an application, we prove (under mild hypotheses) that a positive proportion of prime conductor quadratic twists of E have the same 2-Selmer group.

引用

页码：1633 / 1659

页数：27

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