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Computation on elliptic curves with complex multiplication

Part of: Number theory Arithmetic algebraic geometry Curves

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 [email protected]
Patrick Corn
Affiliation:
Virtu Financial, Austin 78746, USA email [email protected]
Alex Rice
Affiliation:
Bucknell University, Lewisburg 17837, USA email [email protected]
James Stankewicz
Affiliation:
University of Copenhagen, DK-2100 Copenhagen, Denmark email [email protected]

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
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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