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

• Autorzy: Takeshi Hibino , Atsuki Umegaki
• Języki publikacji: EN

Kategorie tematyczne

• 11G05: Elliptic curves over global fields
• 11G18: Arithmetic aspects of modular and Shimura varieties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 88
• Numer: 2
• Strony: 181-190

Daty

wydano

1999

otrzymano

1998-05-05

poprawiono

1998-09-29

Twórcy

autor

Takeshi Hibino

• Advanced Research Institute for Science and Engineering, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169, Japan

autor

Atsuki Umegaki

• Department of Mathematics, School of Science and Engineering, Waseda University, Tokyo, Japan

Bibliografia

• [1] J. Cremona, Algorithm for Modular Elliptic Curves, 2nd ed., Cambridge Univ. Press, Cambridge, 1997.
• [2] P. Deligne et M. Rapoport, Les schémas de modules de courbes elliptiques, Lecture Notes in Math. 349, Springer, New York, 1986, 143-316.
• [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.
• [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.