Number fields generated by the 3-torsion points of an elliptic curve
Identifieur interne : 000160 ( Main/Exploration ); précédent : 000159; suivant : 000161Number fields generated by the 3-torsion points of an elliptic curve
Auteurs : Andrea Bandini [Italie] ; Laura Paladino [Italie]Source :
- Monatshefte für Mathematik [ 0026-9255 ] ; 2012-11-01.
English descriptors
- KwdEn :
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:
DOI: 10.1007/s00605-012-0377-x
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 000711
- to stream Istex, to step Curation: 000711
- to stream Istex, to step Checkpoint: 000126
- to stream Main, to step Merge: 000160
- to stream Main, to step Curation: 000160
Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Number fields generated by the 3-torsion points of an elliptic curve</title><author><name sortKey="Bandini, Andrea" sort="Bandini, Andrea" uniqKey="Bandini A" first="Andrea" last="Bandini">Andrea Bandini</name></author><author><name sortKey="Paladino, Laura" sort="Paladino, Laura" uniqKey="Paladino L" first="Laura" last="Paladino">Laura Paladino</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:21D1E1C0533F300C3493CB96B180454295AF1677</idno><date when="2012" year="2012">2012</date><idno type="doi">10.1007/s00605-012-0377-x</idno><idno type="url">https://api.istex.fr/document/21D1E1C0533F300C3493CB96B180454295AF1677/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">000711</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000711</idno><idno type="wicri:Area/Istex/Curation">000711</idno><idno type="wicri:Area/Istex/Checkpoint">000126</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000126</idno><idno type="wicri:doubleKey">0026-9255:2012:Bandini A:number:fields:generated</idno><idno type="wicri:Area/Main/Merge">000160</idno><idno type="wicri:Area/Main/Curation">000160</idno><idno type="wicri:Area/Main/Exploration">000160</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Number fields generated by the 3-torsion points of an elliptic curve</title><author><name sortKey="Bandini, Andrea" sort="Bandini, Andrea" uniqKey="Bandini A" first="Andrea" last="Bandini">Andrea Bandini</name><affiliation wicri:level="1"><country xml:lang="fr">Italie</country><wicri:regionArea>Dipartimento di Matematica, Università degli Studi di Parma, Parco Area delle Scienze, 53/A, 43124, Parma</wicri:regionArea><wicri:noRegion>Parma</wicri:noRegion></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Italie</country></affiliation></author><author><name sortKey="Paladino, Laura" sort="Paladino, Laura" uniqKey="Paladino L" first="Laura" last="Paladino">Laura Paladino</name><affiliation wicri:level="1"><country xml:lang="fr">Italie</country><wicri:regionArea>Dipartimento di Matematica, Università della Calabria, via Ponte Pietro Bucci, Cubo 30B, 87036, Arcavacata di Rende (CS)</wicri:regionArea><wicri:noRegion>Arcavacata di Rende (CS)</wicri:noRegion></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Italie</country></affiliation></author></analytic><monogr></monogr><series><title level="j">Monatshefte für Mathematik</title><title level="j" type="abbrev">Monatsh Math</title><idno type="ISSN">0026-9255</idno><idno type="eISSN">1436-5081</idno><imprint><publisher>Springer Vienna</publisher><pubPlace>Vienna</pubPlace><date type="published" when="2012-11-01">2012-11-01</date><biblScope unit="volume">168</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="157">157</biblScope><biblScope unit="page" to="181">181</biblScope></imprint><idno type="ISSN">0026-9255</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0026-9255</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Elliptic curves</term><term>Torsion points</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml: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.</div></front></TEI><affiliations><list><country><li>Italie</li></country></list><tree><country name="Italie"><noRegion><name sortKey="Bandini, Andrea" sort="Bandini, Andrea" uniqKey="Bandini A" first="Andrea" last="Bandini">Andrea Bandini</name></noRegion><name sortKey="Bandini, Andrea" sort="Bandini, Andrea" uniqKey="Bandini A" first="Andrea" last="Bandini">Andrea Bandini</name><name sortKey="Paladino, Laura" sort="Paladino, Laura" uniqKey="Paladino L" first="Laura" last="Paladino">Laura Paladino</name><name sortKey="Paladino, Laura" sort="Paladino, Laura" uniqKey="Paladino L" first="Laura" last="Paladino">Laura Paladino</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000160 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000160 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Mathematiques
|area= BourbakiV1
|flux= Main
|étape= Exploration
|type= RBID
|clé= ISTEX:21D1E1C0533F300C3493CB96B180454295AF1677
|texte= Number fields generated by the 3-torsion points of an elliptic curve
}}
| This area was generated with Dilib version V0.6.33. |  |