Families of elliptic curves with rational torsion points of even order

Boris M. Bekker; Yuri G. Zarhin

doi:10.1090/conm/724/14582

Families of elliptic curves with rational torsion points of even order

Boris M. Bekker, Yuri G. Zarhin

Mathematics

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1 Scopus citations

Abstract

We construct explicitly versal families of elliptic curves with rational points of order 4, 6, 8, 10, and 12, respectively. In the last section, we construct versal families of elliptic curves in characteristic 2 that admit a rational point of order 4 or 8.

Original language	English (US)
Pages (from-to)	1-32
Number of pages	32
Journal	Contemporary Mathematics
Volume	724
DOIs	https://doi.org/10.1090/conm/724/14582
State	Published - 2019

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1090/conm/724/14582

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title = "Families of elliptic curves with rational torsion points of even order",

abstract = "We construct explicitly versal families of elliptic curves with rational points of order 4, 6, 8, 10, and 12, respectively. In the last section, we construct versal families of elliptic curves in characteristic 2 that admit a rational point of order 4 or 8.",

author = "Bekker, {Boris M.} and Zarhin, {Yuri G.}",

note = "Funding Information: The second author was partially supported by Simons Foundation #585711. Funding Information: The second author was partially supported by Simons Foundation Collaboration grant #585711. Publisher Copyright: {\textcopyright} 2019 American Mathematical Society.",

year = "2019",

doi = "10.1090/conm/724/14582",

language = "English (US)",

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pages = "1--32",

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publisher = "American Mathematical Society",

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T1 - Families of elliptic curves with rational torsion points of even order

AU - Bekker, Boris M.

AU - Zarhin, Yuri G.

N1 - Funding Information: The second author was partially supported by Simons Foundation #585711. Funding Information: The second author was partially supported by Simons Foundation Collaboration grant #585711. Publisher Copyright: © 2019 American Mathematical Society.

PY - 2019

Y1 - 2019

N2 - We construct explicitly versal families of elliptic curves with rational points of order 4, 6, 8, 10, and 12, respectively. In the last section, we construct versal families of elliptic curves in characteristic 2 that admit a rational point of order 4 or 8.

AB - We construct explicitly versal families of elliptic curves with rational points of order 4, 6, 8, 10, and 12, respectively. In the last section, we construct versal families of elliptic curves in characteristic 2 that admit a rational point of order 4 or 8.

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U2 - 10.1090/conm/724/14582

DO - 10.1090/conm/724/14582

M3 - Article

AN - SCOPUS:85106561145

SN - 0271-4132

VL - 724

SP - 1

EP - 32

JO - Contemporary Mathematics

JF - Contemporary Mathematics

ER -

Families of elliptic curves with rational torsion points of even order

Abstract

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