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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Minimal torsion in isogeny classes of elliptic curves
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by Raymond Ross PDF
Trans. Amer. Math. Soc. 344 (1994), 203-215 Request permission


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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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 344 (1994), 203-215
  • MSC: Primary 11G05; Secondary 11G07
  • DOI:
  • MathSciNet review: 1250824