161
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

A Table of Elliptic Curves over the Cubic Field of Discriminant–23

, , &

References

  • [Atkin and Lehner 70] A. O. L. Atkin and J. Lehner. “Hecke Operators on Γ0(m).” Math. Ann. 185 (1970), 134–160.
  • [Bektemirov et al. 07] Baur Bektemirov, Barry Mazur, William Stein, and Mark Watkins. “Average Ranks of Elliptic Curves: Tension between Data and Conjecture.” Bull. Amer. Math. Soc. (N.S.) 44 (2007), 233–254.
  • [Billerey 11] Nicolas Billerey. “Critères d’irréductibilité pour les représentations des courbes elliptiques.” Int. J. Number Theory 7 (2011), 1001–1032.
  • [Bober et al. 12] Jon Bober, Alyson Deines, Ariah Klages-Mundt, Benjamin LeVeque, R. Andrew Ohana, Ashwath Rabindranath, Paul Sharaba, and William Stein. “A Database of Elliptic Curves over Q(5): First Report.” To appear in Algorithmic Number Theory Symposium X, 2012.
  • [Borel and Serre 73] A. Borel and J.-P. Serre. “Corners and Arithmetic Groups.” Comm. Math. Helv. 48 (1973), 436–491.
  • [Casselman 73a] William Casselman. “On Some Results of Atkin and Lehner.” Math. Ann. 201 (1973), 301–314.
  • [Casselman 73b] William Casselman. “The Restriction of a Representation of GL2(k) to GL 2(o).” Math. Ann. 206 (1973), 311–318.
  • [Cremona 84] J. E. Cremona. “Hyperbolic Tessellations, Modular Symbols, and Elliptic Curves over Complex Quadratic Fields.” Compositio Math. 51 (1984), 275–324.
  • [Cremona 97] J. E. Cremona. Algorithms for Modular Elliptic Curves, second ed. Cambridge University Press, 1997.
  • [Cremona and Aranés 14] J. E. Cremona and M. T. Aranés. “Congruence Subgroups, Cusps and Manin Symbols over Number Fields.” In Computations with Modular Forms, edited by G. Boeckle and G. Wiese, Contributions in Mathematical and Computational Sciences 6, pp. 109–127. Springer, 2014.
  • [Cremona and Lingham 07] J. E. Cremona and M. P. Lingham. “Finding All Elliptic Curves with Good Reduction outside a Given Set of Primes.” Experiment. Math. 16 (2007), 303–312.
  • [Dembélé 08] Lassina Dembélé. “An Algorithm for Modular Elliptic Curves over Real Quadratic Fields.” Experiment. Math. 17 (2008), 427–438.
  • [Franke 98] Jens Franke. “Harmonic Analysis in Weighted L2-Spaces.” Ann. Sci. École Norm. Sup. (4) 31 (1998), 181–279.
  • [Gunnells and Yasaki 13] Paul E. Gunnells and Dan Yasaki. “Modular Forms and Elliptic Curves over the Cubic Field of Discriminant −23.” Int. J. Number Theory 9 (2013), 53–76.
  • [Gunnells et al. 13] Paul E. Gunnells, Farshid Hajir, and Dan Yasaki. “Modular Forms and Elliptic Curves over the Field of Fifth Roots of Unity.” Exp. Math. 22 (2013), 203–216.
  • [Harder 87] G. Harder. “Eisenstein Cohomology of Arithmetic Groups: The Case GL2.” Invent. Math. 89 (1987), 37–118.
  • [Harder 91] G. Harder. “Eisenstein Cohomology of Arithmetic Groups and Its Applications to Number Theory.” In Proceedings of the International Congress of Mathematicians, (Kyoto, 1990) (Tokyo), Vol. I, II. Math. Soc. Japan, pp. 779–790, 1991.
  • [Katz 81] Nicholas M. Katz. “Galois Properties of Torsion Points on Abelian Varieties.” Invent. Math. 62 (1981), 481–502.
  • [Klages-Mundt 12] A. Klages-Mundt. A Database of Elliptic Curves over Complex Cubic Fields. Available online (https://www.amherst.edu/users/K/aklagesmundt12), 2012.
  • [Koecher 60] Max Koecher. “Beiträge zu einer Reduktionstheorie in Positivitätsbereichen. I.” Math. Ann. 141 (1960), 384–432.
  • [Kubert 76] Daniel Sion Kubert. “Universal Bounds on the Torsion of Elliptic Curves.” Proc. London Math. Soc. (3) 33 (1976), 193–237.
  • [Mazur 78] B. Mazur. “Rational Isogenies of Prime Degree” (with an appendix by D. Goldfeld). Invent. Math. 44 (1978), 129–162.
  • [Najman 12] Filip Najman. “Torsion of Elliptic Curves over Cubic Fields.” J. Number Theory 132 (2012), 26–36.
  • [Scholze 13] P. Scholze. “On Torsion in the Cohomology of Locally Symmetric Varieties.” Preprint, 2013.
  • [Silverman 92] Joseph H. Silverman. The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics 106. Springer, 1992.
  • [Stein and Watkins 02] William A. Stein and Mark Watkins. “A Database of Elliptic Curves: First Report.” In Algorithmic Number Theory (Sydney, 2002), Lecture Notes in Comput. Sci. 2369, pp. 267–275. Springer, 2002.

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.