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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Minimal torsion in isogeny classes of elliptic curves


Author: Raymond Ross
Journal: Trans. Amer. Math. Soc. 344 (1994), 203-215
MSC: Primary 11G05; Secondary 11G07
MathSciNet review: 1250824
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Abstract: Let K be a field finitely generated over its prime field, and let $ w(K)$ denote the number of roots of unity in K. If K is of characteristic 0, then there is an integer D, divisible only by those primes dividing $ w(K)$, such that for any elliptic curve $ E/K$ without complex multiplication over K, there is an elliptic curve $ E\prime/K$ isogenous to E such that $ E\prime{(K)_{{\text{tors}}}}$ is of order dividing D. In case K admits a real embedding, we show $ D = 2$, and a nonuniform result is proved in positive characteristic.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1250824-8
PII: S 0002-9947(1994)1250824-8
Article copyright: © Copyright 1994 American Mathematical Society