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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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An algorithm for finding a minimal Weierstrass equation for an elliptic curve
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by Michael Laska PDF
Math. Comp. 38 (1982), 257-260 Request permission

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
  • John T. Tate, The arithmetic of elliptic curves, Invent. Math. 23 (1974), 179–206. MR 419359, DOI 10.1007/BF01389745
  • 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
  • © Copyright 1982 American Mathematical Society
  • 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