English

Elliptic curves and continued fractions

Number Theory 2023-03-24 v6 Operator Algebras

Abstract

It is proved that the rank of an elliptic curve is one less the arithmetic complexity of the corresponding non-commutative torus. As an illustration, we consider a family of elliptic curves with complex multiplication.

Keywords

Cite

@article{arxiv.1611.00278,
  title  = {Elliptic curves and continued fractions},
  author = {Igor V. Nikolaev},
  journal= {arXiv preprint arXiv:1611.00278},
  year   = {2023}
}

Comments

to appear in Aequationes Mathematicae

R2 v1 2026-06-22T16:38:50.626Z