Families of elliptic curves with rational torsion points of even order
Boris M. Bekker, Yuri G. Zarhin

TL;DR
This paper constructs explicit families of elliptic curves with rational torsion points of specific even orders, advancing understanding of their structure and classification.
Contribution
It provides explicit constructions of versal families of elliptic curves with rational points of orders 4, 6, 8, 10, and 12, building on prior work.
Findings
Explicit families for each torsion order are constructed.
The families are versal, covering all cases up to isomorphism.
Enhances classification of elliptic curves with rational torsion points.
Abstract
This paper is a follow up of arXiv:1702.02255 [math.NT]. We construct explicitly versal families of elliptic curves with rational points of order 4, 6, 8, 10, 12 respectively.
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