Points of order \(p\) on elliptic curves over \(\mathbb Q(\sqrt p)\)

DOI10.1007/BF01457444zbMath0489.14010OpenAlexW2323399966MaRDI QIDQ1166587

Sheldon Kamienny

Publication date: 1982

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/182892

zbMATH Keywords

elliptic curvequadratic number fieldEisenstein quotients of jacobiannonexistence of rational point

Mathematics Subject Classification ID

Quadratic extensions (11R11) Rational points (14G05) Special algebraic curves and curves of low genus (14H45) Elliptic curves (14H52) Global ground fields in algebraic geometry (14G25)

Related Items (8)

Torsion points on elliptic curves over all quadratic fields ⋮ Level structures on abelian varieties and Vojta’s conjecture ⋮ Torsion points on elliptic curves over fields of low degree ⋮ p-torsion in elliptic curves over subfields of \({\mathbb Q}(\mu _ p)\) ⋮ Points on Shimura curves over fields of even degree ⋮ Torsion points on elliptic curves and \(q\)-coefficients of modular forms ⋮ Sur la nature non-cyclotomique des points d'ordre fini des courbes elliptiques. (On the noncyclotomic nature of finite-order points of elliptic curves). With an appendix by E. Kowalski and P. Michel ⋮ On the torsion subgroups of elliptic curves over toally real fields

Cites Work

• Unnamed Item
• Modular curves and the class group of \(\mathbb{Q} (\zeta_p)\)
• Modular curves and the Eisenstein ideal
• On J//1(p) and the conjecture of Birch and Swinnerton-Dyer
• Good reduction of abelian varieties
• Rational points of Abelian varieties with values in towers of number fields
• Les Schémas de Modules de Courbes Elliptiques
• Group schemes of prime order

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