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Original Articles

The selmer groups of elliptic curves and the ideal class groups of quadratic fields

Pages 2157-2167 | Received 01 Aug 1996, Published online: 27 Jun 2007

References

  • Chen , Y-M. J. 1993 . Descent via 3-Isogenies On Elliptic Curves , Brown University . Ph. D. thesis
  • Cassels , J.W.S. 1965 . Arithmetic on curves of genus 1 . J. reign Angew. Math. , 217 : 180 – 199 .
  • Cox , D. 1989 . Primes of the Form x2+ ny2, Fermat, Class Fields Theory. and Complex Multiplication , Wiley-Interscience .
  • Frey , G. 1975 . Die Klassgruppe Quadratischer und Kubischer Zahlkörper und die Selmer Gruppen Gewisser Elliptische Kurven . Manuscr. Math. , 16 : 333 – 362 .
  • Nekevá[d] , J. 1990 . Class Number of Quadratic Fields and Shimura's Correspondence . Math. Ann. , 287 : 577 – 594 .
  • Scholz , A. 1987 . Über die Beziehung der Klassenzahlen quadratischer Körper zueinander . J. Reine Angew Math. , 89 : 327 – 560 .
  • Serre , J-P. 1979 . Local Field , Springer-Verlag .
  • Silverman , J. 1985 . The Arithmetic of Elliptic Curves , Springer-Verlag .
  • Tate , J. 1975 . Algorithm for Determining the Type of a Singular Fiber in an Elliptic Pencil , Vol. 476 , 33 – 52 . New York, Berlin : Lect. Notes Math. . Heidelberg

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