论文信息 - Weierstrass equations and the minimal discriminant of an elliptic curve

Weierstrass equations and the minimal discriminant of an elliptic curve

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.

Joseph H. Silverman | J. Silverman

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[2] A. Fröhlich. Discriminants of algebraic number fields , 1960 .

[3] A. Fröhlich. The discriminants of relative extensions and the existence of integral bases , 1960 .