Vol. 108, No. 2, 1983

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Reduction of elliptic curves over imaginary quadratic number fields

Roelof Jacobus Stroeker

Vol. 108 (1983), No. 2, 451–463
Abstract

It is shown that an elliptic curve defined over a complex quadratic field K, having good reduction at all primes, does not have a global minimal (Weierstrass) model. As a consequence of a theorem of Setzer it then follows that there are no elliptic curves over K having good reduction everywhere in case the class number of K is prime to 6.

Mathematical Subject Classification 2000
Primary: 14G25
Secondary: 11G05, 14K07
Milestones
Received: 4 November 1980
Published: 1 October 1983
Authors
Roelof Jacobus Stroeker