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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Merriman, J. R. and Smart, N. P. 1993. Curves of genus 2 with good reduction away from 2 with a rational Weierstrass point. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 114, Issue. 02, p. 203.


    Pinch, R. G. E. 1987. Elliptic curves with good reduction away from 3. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 101, Issue. 03, p. 451.


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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 100, Issue 3
  • November 1986, pp. 435-457

Elliptic curves with good reduction away from 2: II

  • R. G. E. Pinch (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100066196
  • Published online: 24 October 2008
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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