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Computation on elliptic curves with complex multiplication

Part of: Curves Number theory Arithmetic algebraic geometry

Published online by Cambridge University Press:  01 October 2014

Pete L. Clark ,
Patrick Corn ,
Alex Rice  and
James Stankewicz
Pete L. Clark
Affiliation:
University of Georgia, Athens 30602, USA email plclark@gmail.com
Patrick Corn
Affiliation:
Virtu Financial, Austin 78746, USA email patrickcorn@gmail.com
Alex Rice
Affiliation:
Bucknell University, Lewisburg 17837, USA email arice2386@gmail.com
James Stankewicz
Affiliation:
University of Copenhagen, DK-2100 Copenhagen, Denmark email stankewicz@gmail.com

Abstract

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We give the complete list of possible torsion subgroups of elliptic curves with complex multiplication over number fields of degree 1–13. Additionally we describe the algorithm used to compute these torsion subgroups and its implementation.

MSC classification

Secondary: 11-04: Explicit machine computation and programs (not the theory of computation or programming) 11G05: Elliptic curves over global fields 11G15: Complex multiplication and moduli of abelian varieties 14H52: Elliptic curves

Information

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 17 , Issue 1 , 2014 , pp. 509 - 535
Copyright
© The Author(s) 2014 

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