# 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

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top## How to cite

topTakeshi 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

top- [1] J. Cremona, Algorithm for Modular Elliptic Curves, 2nd ed., Cambridge Univ. Press, Cambridge, 1997. Zbl0872.14041
- [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] N. Elkies, A remark on elliptic K-curves, preprint, 1993.
- [4] B. Gross, Arithmetic on Elliptic Curves with Complex Multiplication, Lecture Notes in Math. 776, Springer, New York, 1980.
- [5] Y. Hasegawa, K. Hashimoto and F. Momose, Modular Conjecture for ℚ-curves and QM-curves, preprint, 1996.
- [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] K. Ribet, Abelian varieties over ℚ and modular forms, in: Algebra and Topology 1992 (Taejŏn), KAIST, 1992, 53-79.
- [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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