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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.

References [Enhancements On Off] (What's this?)

  • [1] John T. Tate, The arithmetic of elliptic curves, Invent. Math. 23 (1974), 179–206. MR 419359, https://doi.org/10.1007/BF01389745
  • [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