zbMATH — the first resource for mathematics

Addendum to a paper of Harada and Lang. (English) Zbl 0759.11021
[Cf. K. Harada and 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 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].

11G05 Elliptic curves over global fields
11Y16 Number-theoretic algorithms; complexity
14H52 Elliptic curves
14Q05 Computational aspects of algebraic curves
Full Text: DOI
[1] Hancock, H, Lectures on the theory of elliptic functions, (1958), Dover New York
[2] Harada, K; Lang, M.L, Some elliptic curves arising from the Leech lattice, J. algebra, 125, 298-310, (1989) · Zbl 0715.11029
[3] Mordell, L.J, Diophantine equations, (1969), Academic Press London · Zbl 0188.34503
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.