Elliptic curves with large torsion and positive rank over number fields of small degree and ECM factorization

Details Elliptic curves with large torsion and positive rank over number fields of small degree and ECM factorization Elliptic curves with large torsion and positive rank over number fields of small degree and ECM factorization

2011-12-31

arxiv.org/abs/1201.0266v1

Mathematics

Number Theory

10 pages

Scientific paper

In this paper, we present several methods for construction of elliptic curves
with large torsion group and positive rank over number fields of small degree.
We also discuss potential applications of such curves in the elliptic curve
factorization method (ECM).

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