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Elliptic curves over the rationals with bad reduction at only one prime


Authors: Bas Edixhoven, Arnold de Groot and Jaap Top
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
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Abstract | References | Similar Articles | Additional Information

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.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1990-0995209-4
Article copyright: © Copyright 1990 American Mathematical Society