## 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

## 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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## Additional Information

- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**344**(1994), 203-215 - MSC: Primary 11G05; Secondary 11G07
- DOI: https://doi.org/10.1090/S0002-9947-1994-1250824-8
- MathSciNet review: 1250824