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On the units generated by Weierstrass forms

Part of: Computational number theory Algebraic number theory: global fields Arithmetic algebraic geometry

Published online by Cambridge University Press:  01 August 2014

Ömer Küçüksakallı
Ömer Küçüksakallı*
Affiliation:
Department of Mathematics , Middle East Technical University, 06800 Ankara, Turkey email komer@metu.edu.tr

Abstract

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There is an algorithm of Schoof for finding divisors of class numbers of real cyclotomic fields of prime conductor. In this paper we introduce an improvement of the elliptic analogue of this algorithm by using a subgroup of elliptic units given by Weierstrass forms. These elliptic units which can be expressed in terms of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}x$-coordinates of points on elliptic curves enable us to use the fast arithmetic of elliptic curves over finite fields.

MSC classification

Secondary: 11G16: Elliptic and modular units 11R29: Class numbers, class groups, discriminants 11Y40: Algebraic number theory computations
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 17 , Special Issue A: Algorithmic Number Theory Symposium XI , 2014 , pp. 303 - 313
Copyright
© The Author 2014 

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