Congruent numbers and the Tate-Shafarevich group of the elliptic curve y[2]=x[3]-n[2]x

[目次]

  • Contents / p1
  • Introduction / p2
  • Acknowledgements / p4
  • Notations / p5
  • I.Preliminaries / p1
  • §1.Congruent numbers and elliptic curves / p1
  • §2.Weierstraß models of E/Q / p2
  • §3.The covariants c₄ and c₆ of E/Q / p4
  • §4.Minimal models of En and E′n / p7
  • §5.L-functions and the Birch and Swinnerton-Dyer conjecture / p8
  • II.Computations
  • §1.Computation of the rth derivative [数式](En,1) / p11
  • §2.Rank computation method / p13
  • §3.Algorithm for solution search / p20
  • §4.Computational results / p25
  • III.Local-Global Considerations / p27
  • §1.Local solvability of the quartic / p27
  • §2.The rank of E₂₃₇₉ / p29
  • §3.The φ and ψ- parts of the Tate-Shafarevich groups / p34
  • §4.Tate's algorithm / p37
  • §5.Ratio of orders of III and III′ / p40
  • Appendix 1:Tables / p42
  • Appendix 2:Programs / p57
  • References / p60

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書名 Congruent numbers and the Tate-Shafarevich group of the elliptic curve y[2]=x[3]-n[2]x
著作者等 Fidel
Nemenzo
Nemenzo, Fidel
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