Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Elliptic curves over the rationals with bad reduction at only one prime
HTML articles powered by AMS MathViewer

by Bas Edixhoven, Arnold de Groot and Jaap Top PDF
Math. Comp. 54 (1990), 413-419 Request permission

Abstract:

A list is given of elliptic curves over Q having additive reduction at exactly one prime. It is also proved that for primes congruent to 5 modulo 12, no such curves having potentially good reduction exist. This enables one to find in a number of cases a complete list of all elliptic curves with bad reduction at only one prime.
References
  • B. J. Birch and W. Kuyk (eds.), Modular functions of one variable. IV, Lecture Notes in Mathematics, Vol. 476, Springer-Verlag, Berlin-New York, 1975. MR 0376533
  • Armand Brumer and Kenneth Kramer, The rank of elliptic curves, Duke Math. J. 44 (1977), no. 4, 715–743. MR 457453
    • S. J. Edixhoven, Stable models of modular curves and applications, Ph.D. Thesis, Math. Inst., Univ. of Utrecht, 1989.
  • Benedict H. Gross, Arithmetic on elliptic curves with complex multiplication, Lecture Notes in Mathematics, vol. 776, Springer, Berlin, 1980. With an appendix by B. Mazur. MR 563921
  • B. Mazur, Rational isogenies of prime degree (with an appendix by D. Goldfeld), Invent. Math. 44 (1978), no. 2, 129–162. MR 482230, DOI 10.1007/BF01390348
  • J.-F. Mestre, La méthode des graphes. Exemples et applications, Proceedings of the international conference on class numbers and fundamental units of algebraic number fields (Katata, 1986) Nagoya Univ., Nagoya, 1986, pp. 217–242 (French). MR 891898
    • T. Nagel, Über die rationalen Punkte auf einigen kubischen Kurven, Tôhoku Math. J. 24 (1925), 48-53. M. T. Nagell, L’analyse indéterminée de degré supérieur, Mémorial des Sciences Mathématiques 39 (1929).
  • Bennett Setzer, Elliptic curves of prime conductor, J. London Math. Soc. (2) 10 (1975), 367–378. MR 371904, DOI 10.1112/jlms/s2-10.3.367
  • Joseph H. Silverman, The arithmetic of elliptic curves, Graduate Texts in Mathematics, vol. 106, Springer-Verlag, New York, 1986. MR 817210, DOI 10.1007/978-1-4757-1920-8
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 11G05, 11D25
  • Retrieve articles in all journals with MSC: 11G05, 11D25
Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Math. Comp. 54 (1990), 413-419
  • MSC: Primary 11G05; Secondary 11D25
  • DOI: https://doi.org/10.1090/S0025-5718-1990-0995209-4
  • MathSciNet review: 995209