On the explicit models of Shimura's elliptic curves

Ken-ichi SHIOTA

doi:10.2969/jmsj/03840649

Ken-ichi SHIOTA

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JOURNAL FREE ACCESS

1986 Volume 38 Issue 4 Pages 649-659

DOI https://doi.org/10.2969/jmsj/03840649

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Published: 1986 Received: April 01, 1985 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) P. Deligne and M. Rapoport, Les schémas de modules de courbes elliptiques, Lecture Notes in Math., 349, Springer, 1973.
2) H. Ishii, The non-existence of elliptic curves with everywhere good reduction over certain quadratic fields, preprint.
3) I. Miyawaki, Elliptic curves of prime power conductor with Q-rational points of finite order, Osaka J. Math., 10 (1973), 309-323.
4) H. Naganuma, On the coincidence of two Dirichlet series associated with cusp forms of Hecke's “Neben”.type and Hilbert modular forms over a real quadratic field, J. Math. Soc. Japan, 25 (1973), 547-555.
5) T. Nakamura, On Shimura's elliptic curve over Q(√<29>), J. Math. Soc. Japan, 36 (1984), 701-707.
6) K. A. Ribet, Endomorphisms of semi-stable abelian varieties over number fields, Ann. of Math., 101 (1975), 555-562.
7) J.-P. Serre, Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math., 15 (1972), 259-331.
8) B. Setzer, Elliptic curves with good reduction everywhere over quadratic fields and having rational j-invariant, Illinois J. Math., 25 (1981), 233-245.
9) G. Shimura, Introduction to the arithmetic theory of automorphic functions, Iwanami Shoten and Princeton Univ. Press, 1971.
10) G. Shimura, Class fields over real quadratic fields and Hecke operators, Ann. of Math., 95 (1972), 130-190.
11) G. Shimura, On the factors of the jacobian variety of a modular function field, J. Math. Soc. Japan, 25 (1973), 523-544.
12) R. J. Stroeker, Elliptic curves defined over imaginary quadratic number fields, Thesis, University of Amsterdam, 1975.

Right : [1] P. Deligne and M. Rapoport, Les schémas de modules de courbes elliptiques, Lecture Notes in Math., 349, Springer, 1973.
[2] H. Ishii, The non-existence of elliptic curves with everywhere good reduction over certain quadratic fields, preprint.
[3] I. Miyawaki, Elliptic curves of prime power conductor with Q-rational points of finite order, Osaka J. Math., 10 (1973), 309-323.
[4] H. Naganuma, On the coincidence of two Dirichlet series associated with cusp forms of Hecke's “Neben”.type and Hilbert modular forms over a real quadratic field, J. Math. Soc. Japan, 25 (1973), 547-555.
[5] T. Nakamura, On Shimura's elliptic curve over Q(√<29>), J. Math. Soc. Japan, 36 (1984), 701-707.
[6] K. A. Ribet, Endomorphisms of semi-stable abelian varieties over number fields, Ann. of Math., 101 (1975), 555-562.
[7] J. -P. Serre, Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math., 15 (1972), 259-331.
[8] B. Setzer, Elliptic curves with good reduction everywhere over quadratic fields and having rational j-invariant, Illinois J. Math., 25 (1981), 233-245.
[9] G. Shimura, Introduction to the arithmetic theory of automorphic functions, Iwanami Shoten and Princeton Univ. Press, 1971.
[10] G. Shimura, Class fields over real quadratic fields and Hecke operators, Ann. of Math., 95 (1972), 130-190.
[11] G. Shimura, On the factors of the jacobian variety of a modular function field, J. Math. Soc. Japan, 25 (1973), 523-544.
[12] R. J. Stroeker, Elliptic curves defined over imaginary quadratic number fields, Thesis, University of Amsterdam, 1975.

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