27
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Symmetric Squares of Elliptic Curves: Rational Points and Selmer Groups

Pages 457-464 | Published online: 03 Apr 2012

REFERENCES

  • Abbes , A. and Ullmo , S. 1996 . “À propos de la conjecture de Manin pour les courbes elliptiques modulaires.” . Compositio Math. , 103 : 269 – 286 . [Abbes and Ullmo 96]
  • Bloch , S. and Kato , K. 1990 . “L-Functions and Tamagawa Numbers of Motives.”. ” . In The Grothendieck Festschrift Volume I 333 – 400 . Boston , MA : Birkhäuser Boston. . [Bloch and Kato 90], Progress in Mathematics 86
  • Cremona , J. E. and Mazur , B. 2000 . “Visualizing Elements in the Shafarevich-Tate Group.” . Experiment. Math. , : 13 – 28 . [Cremona and Mazur 00]
  • Cremona , J. E. and Mazur , B. 2002 . “Visible Evidence for the Birch and Swinnerton Dyer Conjecture for Modular Abelian Varieties of Rank Zero.” [Cremona and Mazur 02], Appendix to A. Agashe and W. Stein. Preprint. Available from World Wide Web: (http://www.modular.fas.harvard.edu/papers/shacomp
  • Coates , J. and Schmidt , C. G. 1987 . “Iwasawa Theory for the Symmetric Square of an Elliptic Curve.” . J. Reine Angew. Math. , 375/376 : 104 – 156 . [Coates and Schmidt 87]
  • Diamond , F. , Flach , M. and Guo , L. 2001 . “On the Bloch-Kato Conjecture for Adjoint Motives of Modular Forms.” . Math. Res. Lett. , : 237 – 242 . [Diamond et al. 01a]
  • Diamond , F. , Flach , M. and Guo , L. 2001 . “Adjoint Motives of Modular Forms and the Tamagawa Number Conjecture.” [Diamond et al. 01b], Preprint. Available from World Wide Web: (http://www.andromeda.rutgers.edu/~liguo/lgpapers.html
  • Dummigan , N. 2001 . “Symmetric Square - Functions and Shafarevich-Tate Groups.” . Experiment. Math. , 10 : 383 – 400 . [Dummigan 01a]
  • Dummigan , N. “Values of a Hilbert Modular Symmetric Square -Function.” [Dummigan 01b], In Preparation
  • Flach , M. 1993 . “On the Degree of Modular Parametrisations.”. ” . In Séminaire de Theórie des Nombres, Paris 1991–92 Edited by: David , S. 23 – 36 . Boston , MA : Birkhäuser Boston. . [Flach 93], Progress in Mathematics 116
  • Flach , M. 1992 . “A Finiteness Theorem for the Symmetric Square of an Elliptic Curve.” . Invent. Math. , 109 : 307 – 327 . [Flach 92]
  • Flach , M. 1990 . “A Generalisation of the Cassels-Tate Pairing.” . J. reine angew. Math. , 412 : 113 – 127 . [Flach 90]
  • Mazur , B. 1978 . “Rational Isogenies of Prime Degree.” . Invent. Math. , 44 : 129 – 62 . [Mazur 78]
  • Rankin , R. A. 1939 . “Contributions to the Theory of Ramanujan's Function τ(n) and Similar Arithmetical Functions.” . Proc. Cambridge Philos. Soc. , 35 : 351 – 372 . [Rankin 39]
  • Shimura , G. 1976 . “The Special Values of the Zeta Functions Associated with Cusp Forms.” . Comm. Pure Appl. Math. , 29 : 783 – 804 . [Shimura 76]
  • Serre , J.-P. 1972 . “Propriétés galoisiennes des points d'ordre fini des courbes elliptiques” . Invent. Math. , 15 : 259 – 331 . [Serre 72]
  • Silverman , J. H. 1986 . The Arithmetic of Elliptic Curves New York : Springer-Verlag. . [Silverman 86], GTM 106
  • Silverman , J. H. 1994 . Advanced Topics in the Arithmetic of Elliptic Curves, GTM 151 New York : Springer-Verlag. . [Silverman 94]
  • Taylor , R. and Wiles , A. 1995 . “Ring- Theoretic Properties of Certain Hecke Algebras.” . Ann. Math. , 141 : 553 – 572 . [Taylor and Wiles 95]
  • Watkins , M. 2002 . “Computing the Modular Degree of an Elliptic Curve.” [Watkins 02], Preprint. Available from World Wide Web, http://www.math.psu.edu/watkins/moddeg.ps
  • Wiles , A. 1995 . “Modular Elliptic Curves and Fermat's Last Theorem.” . Ann. Math. , 141 : 443 – 551 . [Wiles 95]

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.