Large Shafarevich–Tate groups over quadratic number fields

Myungjun Yu

doi:10.1016/j.jnt.2018.12.012

Large Shafarevich–Tate groups over quadratic number fields

Myungjun Yu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let E be an elliptic curve over the rational field Q. Let K be a quadratic extension of Q. We show that (under mild conditions on E) for every r>0, there are infinitely many quadratic twists E ^d /Q of E/Q such that (Figure presented.).

Original language	English
Pages (from-to)	98-109
Number of pages	12
Journal	Journal of Number Theory
Volume	199
DOIs	https://doi.org/10.1016/j.jnt.2018.12.012
Publication status	Published - 2019 Jun

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Publisher Copyright:
© 2019 Elsevier Inc.

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jnt.2018.12.012

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title = "Large Shafarevich–Tate groups over quadratic number fields",

abstract = " Let E be an elliptic curve over the rational field Q. Let K be a quadratic extension of Q. We show that (under mild conditions on E) for every r>0, there are infinitely many quadratic twists E d /Q of E/Q such that (Figure presented.).",

author = "Myungjun Yu",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2019",

month = jun,

doi = "10.1016/j.jnt.2018.12.012",

language = "English",

volume = "199",

pages = "98--109",

journal = "Journal of Number Theory",

issn = "0022-314X",

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AU - Yu, Myungjun

PY - 2019/6

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N2 - Let E be an elliptic curve over the rational field Q. Let K be a quadratic extension of Q. We show that (under mild conditions on E) for every r>0, there are infinitely many quadratic twists E d /Q of E/Q such that (Figure presented.).

AB - Let E be an elliptic curve over the rational field Q. Let K be a quadratic extension of Q. We show that (under mild conditions on E) for every r>0, there are infinitely many quadratic twists E d /Q of E/Q such that (Figure presented.).

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DO - 10.1016/j.jnt.2018.12.012

M3 - Article

AN - SCOPUS:85060618277

SN - 0022-314X

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EP - 109

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Large Shafarevich–Tate groups over quadratic number fields

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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