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Bounded torsion of elliptic curves

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Abstract

An explicit bound is obtained for the torsion of elliptic curves over the field of rational numbers. Let Γ be an elliptic curve over the field of rational numbers R, and Qm a primitive R-point of order m on it; here m is a prime or a double prime. Hence if m=2p, then p ≤ 509, whereas if m=p, then p < 6144.

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Literature cited

  1. V. A. Dem'yanenko, “Torsion of elliptic curves,” Izv. AN SSSR, Ser. Matem.,35, 280–307 (1971).

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  2. V. A. Dem'yanenko, “Torsion points of elliptic curves,” Izv. AN SSSR, Ser. Matem.,34, 757–774 (1970).

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Academy of Sciences of the USSR, USSR

    V. A. Dem'yanenko

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  1. V. A. Dem'yanenko
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Translated from Matematicheskie Zametki, No. 1, pp. 53–58, July, 1972.

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Dem'yanenko, V.A. Bounded torsion of elliptic curves. Mathematical Notes of the Academy of Sciences of the USSR 12, 464–466 (1972). https://doi.org/10.1007/BF01094392

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  • DOI: https://doi.org/10.1007/BF01094392

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