Addendum to a paper of Harada and Lang
[Cf. \textit{K. Harada} and \textit{M. L. Lang}, J. Algebra 125, 298-310 (1989; Zbl 0715.11029).] The usual proof, by Riemann-Roch, that an elliptic curve can be put into Weierstraß form does not provide a practical algorithm, but appropriate transformations are described, e.g., by \textit{J. W. S. Cassels} [Lectures on Elliptic Curves, Cambridge Univ. Press (1991; Zbl 0752.14033)] for general cubics, quartics, and intersections of two quadric surfaces (with a rational point in each case). The present paper discusses such algorithms for the first two cases. [Author's note: Both these algorithms are included as procedures in ``apecs'' (arithmetic of plane elliptic curves) which is a comprehensive program written in MAPLE intended for free distribution].
scientific article; zbMATH DE number 33062