Computation on Elliptic Curves with Complex Multiplication
Pete L. Clark, Patrick Corn, Alex Rice, James Stankewicz
TL;DR
This paper classifies torsion subgroups of elliptic curves with complex multiplication over number fields of degree 1-13, providing a comprehensive list and an algorithm for their computation.
Contribution
It offers the first complete classification of torsion subgroups for CM elliptic curves over these fields and details an algorithm for their calculation.
Findings
Complete list of torsion subgroups for CM elliptic curves over degree 1-13 fields
Development and implementation of an algorithm to compute these torsion subgroups
Enhanced understanding of the structure of CM elliptic curves over small degree fields
Abstract
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.
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