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Elliptic curves with good reduction away from 2: II

  • R. G. E. Pinch (a1)
Abstract

In this paper we continue the study of elliptic curves defined over a quadratic field with good reduction at primes not dividing 2 begun in [9] (referred to as I). We extend the results of I to show that such a curve must have a point of order 2 also defined over when d = −7, −3, −2, −1, 2, 3 or 5 and list all such curves over .

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[2]B. J. Birch and W. Kuyk (eds.). Modular Functions of One Variable IV. Lecture Notes in Mathematics, vol. 476 (Springer, 1975).

[7]A. Odlyzko . Some analytic estimates of class numbers and discriminants. Invent. Math. 29 (1975), 275286.

[10]M. Pohst . On the computation of number fields of small discriminant. J. Number Theory 14 (1982), 99117.

[11]I. N. Stewart and D. O. Tall . Algebraic Number Theory (Chapman & Hall, 1979).

[13]R. J. Stroeker . Reduction of elliptic curves over imaginary quadratic number fields. Pacific J. Math. 108 (1983), 451463.

[15]T. P. Vaughan . The discriminant of a quadratic extension of an algebraic field. Math. Comp. 40 (1983), 685707.

[16]T. P. Vaughan . Corrigendum to [15]. Math. Comp. 43 (1984), 621.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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