An algorithm for finding a minimal Weierstrass equation for an elliptic curve

Author:
Michael Laska

Journal:
Math. Comp. **38** (1982), 257-260

MSC:
Primary 14K15; Secondary 14-04, 14G25, 14K07

DOI:
https://doi.org/10.1090/S0025-5718-1982-0637305-2

MathSciNet review:
637305

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Abstract: Let *E* be an elliptic curve defined over an algebraic number field *K* and assume that some Weierstrass equation for *E* over *K* is given. Then an algorithm is described which yields a global minimal Weierstrass equation for *E* over *K* provided such a global minimal Weierstrass equation does exist.

**[1]**J. T. Tate, ``The arithmetic of elliptic curves,''*Invent. Math.*, v. 23, 1974, pp. 179-206. MR**0419359 (54:7380)****[2]**J. T. Tate, ``Algorithm for determining the type of singular fiber in an elliptic pencil,''*Modular Functions of One Variable*. IV, Lecture Notes in Math., Vol. 476, Springer-Verlag, Berlin and New York, 1975.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1982-0637305-2

Article copyright:
© Copyright 1982
American Mathematical Society