Potential good reduction of elliptic curves

Authors:
Masanari Kida
Affiliations:
Department of Mathematics, The University of Electro-Communications, Chofu, Tokyo 182-8585, Japan
Venue:
Journal of Symbolic Computation
Year:
2002

Citing 2
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Algorithms for modular elliptic curves

Algorithms for modular elliptic curves
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Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference

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Abstract

We show that there is no elliptic curve defined over the field of rational numbers that attains good reduction at every finite place under quadratic base change. We also give some examples of elliptic curves that acquire good reduction everywhere under cubic or quartic base changes.