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Weierstrass equations and the minimal discriminant of an elliptic curve

Part of: Curves

Published online by Cambridge University Press:  26 February 2010

Joseph H. Silverman
Joseph H. Silverman
Affiliation:
Mathematics Department 2–271, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, U.S.A.
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Extract

Let K be a number field and E/K an elliptic curve. As is well known [3, 4,[ if K has class number 1, then there exists a global minimal Weierstrass equation for E. Our main goal in this paper is to prove the following converse to this statement.

MSC classification

Secondary: 14H45: Special curves and curves of low genus
Type
Research Article
Information
Mathematika , Volume 31 , Issue 2 , December 1984 , pp. 245 - 251
Copyright
Copyright © University College London 1984

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References

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3.Setzer, B.. Elliptic curves over complex quadratic fields. Pacific J. of Math., 74 (1978), 235–250.CrossRefGoogle Scholar
4.Tate, J.. Algorithm for determining the type of a singular fiber in an elliptic pencil. Lecture Notes in Math., 476 (Springer, 1975), 33–52.Google Scholar