BourbakiV1, Istex, Corpus, bibRecord, 000711

Number fields generated by the 3-torsion points of an elliptic curve

Identifieur interne : 000711 ( Istex/Corpus ); précédent : 000710; suivant : 000712

Number fields generated by the 3-torsion points of an elliptic curve

Auteurs : Andrea Bandini ; Laura Paladino

Source :

Monatshefte für Mathematik [ 0026-9255 ] ; 2012-11-01.

RBID : ISTEX:21D1E1C0533F300C3493CB96B180454295AF1677

English descriptors

KwdEn :
- Elliptic curves, Torsion points.

Abstract

Abstract: Let $${{\mathcal{E}}}$$ be an elliptic curve, m a positive number and $${\mathcal{E}[m]}$$ the m-torsion subgroup of $${\mathcal{E}}$$ . Let P 1 = (x 1, y 1), P 2 = (x 2, y 2) form a basis of $${\mathcal{E}[m]}$$ . We prove that $${\mathbb Q(\mathcal{E}[m]) = \mathbb Q(x_1, x_2, \zeta_m, y_1)}$$ in general. For the case m = 3 we provide a description of all the possible extensions $${\mathbb Q(\mathcal{E}[3])}$$ in terms of generators, degree and Galois groups.

Url:

https://api.istex.fr/document/21D1E1C0533F300C3493CB96B180454295AF1677/fulltext/pdf

DOI: 10.1007/s00605-012-0377-x

Links to Exploration step

ISTEX:21D1E1C0533F300C3493CB96B180454295AF1677

Le document en format XML

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 . Let <Emphasis Type="Italic">P</Emphasis>
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 in terms of generators, degree and Galois groups.</Para>
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<originInfo><publisher>Springer Vienna</publisher>
<place><placeTerm type="text">Vienna</placeTerm>
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<dateCreated encoding="w3cdtf">2011-05-05</dateCreated>
<dateIssued encoding="w3cdtf">2012-11-01</dateIssued>
<dateIssued encoding="w3cdtf">2012</dateIssued>
<copyrightDate encoding="w3cdtf">2012</copyrightDate>
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<abstract lang="en">Abstract: Let $${{\mathcal{E}}}$$ be an elliptic curve, m a positive number and $${\mathcal{E}[m]}$$ the m-torsion subgroup of $${\mathcal{E}}$$ . Let P 1 = (x 1, y 1), P 2 = (x 2, y 2) form a basis of $${\mathcal{E}[m]}$$ . We prove that $${\mathbb Q(\mathcal{E}[m]) = \mathbb Q(x_1, x_2, \zeta_m, y_1)}$$ in general. For the case m = 3 we provide a description of all the possible extensions $${\mathbb Q(\mathcal{E}[3])}$$ in terms of generators, degree and Galois groups.</abstract>
<subject lang="en"><genre>Keywords</genre>
<topic>Elliptic curves</topic>
<topic>Torsion points</topic>
</subject>
<classification displayLabel="Mathematics Subject Classification (2010)">11G05</classification>
<classification displayLabel="Mathematics Subject Classification (2010)">12F05</classification>
<relatedItem type="host"><titleInfo><title>Monatshefte für Mathematik</title>
</titleInfo>
<titleInfo type="abbreviated"><title>Monatsh Math</title>
</titleInfo>
<genre type="journal" displayLabel="Archive Journal" authority="ISTEX" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0GLKJH51-B">journal</genre>
<originInfo><publisher>Springer</publisher>
<dateIssued encoding="w3cdtf">2012-10-16</dateIssued>
<copyrightDate encoding="w3cdtf">2012</copyrightDate>
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<topic authority="SpringerSubjectCodes" authorityURI="Mathematics and Statistics">SC10</topic>
</subject>
<subject><genre>Mathematics</genre>
<topic>Mathematics, general</topic>
</subject>
<identifier type="ISSN">0026-9255</identifier>
<identifier type="eISSN">1436-5081</identifier>
<identifier type="JournalID">605</identifier>
<identifier type="JournalSPIN">30023915</identifier>
<identifier type="IssueArticleCount">9</identifier>
<identifier type="VolumeIssueCount">5</identifier>
<part><date>2012</date>
<detail type="volume"><number>168</number>
<caption>vol.</caption>
</detail>
<detail type="issue"><number>2</number>
<caption>no.</caption>
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<extent unit="pages"><start>157</start>
<end>181</end>
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</part>
<recordInfo><recordOrigin>Springer-Verlag Wien, 2012</recordOrigin>
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<identifier type="istex">21D1E1C0533F300C3493CB96B180454295AF1677</identifier>
<identifier type="ark">ark:/67375/VQC-7LN1TP9T-9</identifier>
<identifier type="DOI">10.1007/s00605-012-0377-x</identifier>
<identifier type="ArticleID">377</identifier>
<identifier type="ArticleID">s00605-012-0377-x</identifier>
<accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag, 2012</accessCondition>
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Number fields generated by the 3-torsion points of an elliptic curve

Number fields generated by the 3-torsion points of an elliptic curve

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