On the finiteness of the number of elliptic fields with given degrees of S-units and periodic expansion of √f

Abstract

For a field k of characteristic 0, up to a natural equivalence relation, it is proved that the number of nontrivial elliptic fields k(x)(f) with a periodic expansion of f ∈ k((x)), for which the corresponding elliptic curve contains a k-point of even order less or equal than 18 or k-point of odd order less or equal than 11, is finite. In case k is a quadratic extension of Q, all such fields are found.

Locations

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