A family of elliptic ℚ-curves defined over biquadratic fields and their modularity

Takeshi Hibino; Atsuki Umegaki

Acta Arithmetica (1999)

  • Volume: 88, Issue: 2, page 181-190
  • ISSN: 0065-1036

How to cite

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Takeshi Hibino, and Atsuki Umegaki. "A family of elliptic ℚ-curves defined over biquadratic fields and their modularity." Acta Arithmetica 88.2 (1999): 181-190. <http://eudml.org/doc/207238>.

@article{TakeshiHibino1999,
author = {Takeshi Hibino, Atsuki Umegaki},
journal = {Acta Arithmetica},
language = {eng},
number = {2},
pages = {181-190},
title = {A family of elliptic ℚ-curves defined over biquadratic fields and their modularity},
url = {http://eudml.org/doc/207238},
volume = {88},
year = {1999},
}

TY - JOUR
AU - Takeshi Hibino
AU - Atsuki Umegaki
TI - A family of elliptic ℚ-curves defined over biquadratic fields and their modularity
JO - Acta Arithmetica
PY - 1999
VL - 88
IS - 2
SP - 181
EP - 190
LA - eng
UR - http://eudml.org/doc/207238
ER -

References

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  1. [1] J. Cremona, Algorithm for Modular Elliptic Curves, 2nd ed., Cambridge Univ. Press, Cambridge, 1997. Zbl0872.14041
  2. [2] P. Deligne et M. Rapoport, Les schémas de modules de courbes elliptiques, Lecture Notes in Math. 349, Springer, New York, 1986, 143-316. Zbl0281.14010
  3. [3] N. Elkies, A remark on elliptic K-curves, preprint, 1993. 
  4. [4] B. Gross, Arithmetic on Elliptic Curves with Complex Multiplication, Lecture Notes in Math. 776, Springer, New York, 1980. 
  5. [5] Y. Hasegawa, K. Hashimoto and F. Momose, Modular Conjecture for ℚ-curves and QM-curves, preprint, 1996. 
  6. [6] T. Hibino and A. Umegaki, Families of elliptic ℚ-curves defined over number fields with large degrees, Proc. Japan Acad. Ser. A 74 (1998), 20-24. Zbl0922.11049
  7. [7] K. Ribet, Abelian varieties over ℚ and modular forms, in: Algebra and Topology 1992 (Taejŏn), KAIST, 1992, 53-79. 
  8. [8] G. Shimura, Introduction to the Arithmetic Theory of Automorphic Forms, Publ. Math. Soc. Japan 11, Iwanami Shoten, 1971. Zbl0221.10029

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