Kamienny, Sheldon Torsion points on elliptic curves over all quadratic fields. II. (English) Zbl 0599.14030 Bull. Soc. Math. Fr. 114, 119-122 (1986). [For part I see the preceding review Zbl 0599.14029.] Let p be one of the primes 23, 29, 31, 41, 47, 59, or 71. Let X be the completion of the curve which classifies isomorphism of elliptic curves together with a rational point of order p. Using the fact that X is hyperelliptic with Atkin-Lehner involution the author shows that for any quadratic field K, there is no elliptic curve defined over K containing a K-rational point of order p. Reviewer: K.Lai Cited in 2 ReviewsCited in 7 Documents MSC: 14H45 Special algebraic curves and curves of low genus 11R11 Quadratic extensions 14G05 Rational points 14H25 Arithmetic ground fields for curves 14H52 Elliptic curves Keywords:isomorphism of elliptic curves; rational point of order p Citations:Zbl 0599.14029 PDFBibTeX XMLCite \textit{S. Kamienny}, Bull. Soc. Math. Fr. 114, 119--122 (1986; Zbl 0599.14030) Full Text: DOI Numdam EuDML References: [1] KAMIENNY (S.) . - Torsion points on elliptic curves over all quadratic fields (to appear in Duke Math Journal.) Article | Zbl 0599.14029 · Zbl 0599.14029 [2] MAZUR (B.) . - Modular curves and the Eisenstein ideal . Publications Mathématiques I.H.E.S., Vol. 47, 1978 . Numdam | Zbl 0394.14008 · Zbl 0394.14008 [3] MAZUR (B.) . - On the arithmetic of special values of L functions , Inventiones Math., Vol. 55, 1979 , pp. 207-240. MR 82e:14033 | Zbl 0426.14009 · Zbl 0426.14009 [4] OGG (A.) . - Hyperelliptic modular curves , Bull. Soc. Math. Fr., Vol. 102, 1974 , pp. 449-462. Numdam | MR 51 #514 | Zbl 0314.10018 · Zbl 0314.10018 [5] RAYNAUD (M.) . - Schémas en groupes de type (p, ..., p) , Bull. Soc. Math. Fr., Vol. 102, 1974 , pp. 241-280. Numdam | MR 54 #7488 | Zbl 0325.14020 · Zbl 0325.14020 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.