Tate-Shafarevich groups of the congruent number elliptic curves

Ken Ono

Acta Arithmetica (1997)

  • Volume: 81, Issue: 3, page 247-252
  • ISSN: 0065-1036

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Ken Ono. "Tate-Shafarevich groups of the congruent number elliptic curves." Acta Arithmetica 81.3 (1997): 247-252. <http://eudml.org/doc/207063>.

@article{KenOno1997,
author = {Ken Ono},
journal = {Acta Arithmetica},
keywords = {Tate-Shafarevich groups; congruent number elliptic curves; Birch and Swinnerton-Dyer conjecture},
language = {eng},
number = {3},
pages = {247-252},
title = {Tate-Shafarevich groups of the congruent number elliptic curves},
url = {http://eudml.org/doc/207063},
volume = {81},
year = {1997},
}

TY - JOUR
AU - Ken Ono
TI - Tate-Shafarevich groups of the congruent number elliptic curves
JO - Acta Arithmetica
PY - 1997
VL - 81
IS - 3
SP - 247
EP - 252
LA - eng
KW - Tate-Shafarevich groups; congruent number elliptic curves; Birch and Swinnerton-Dyer conjecture
UR - http://eudml.org/doc/207063
ER -

References

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  1. [B-E-W] B. C. Berndt, R. J. Evans and K. S. Williams, Gauss and Jacobi Sums, Wiley, to appear. Zbl0906.11001
  2. [C] J. E. Cremona, Algorithms for Elliptic Curves, Cambridge Univ. Press, 1992. Zbl0758.14042
  3. [D] L. E. Dickson, History of the Theory of Numbers, Vol. 3, G. E. Strechert & Co., 1934. Zbl60.0817.03
  4. [J] N. Jochnowitz, Congruences between modular forms of half integral weights and implications for class numbers and elliptic curves, preprint. Zbl0536.10022
  5. [M-O] Y. Martin and K. Ono, Eta-quotients and elliptic curves, Proc. Amer. Math. Soc., to appear. Zbl0894.11020
  6. [O-S] K. Ono and C. Skinner, Fourier coefficients of half-integral weight modular forms mod l, preprint. Zbl0907.11017
  7. [R] K. Rubin, Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication, Invent. Math. 89 (1987), 527-560. Zbl0628.14018
  8. [S] J. Silverman, The Arithmetic of Elliptic Curves, Springer, New York, 1986. Zbl0585.14026
  9. [T] J. B. Tunnell, A classical Diophantine problem and modular forms of weight 3/2, Invent. Math. 72 (1983), 323-334. Zbl0515.10013

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