Elliptic curves and continued fractions
arXiv:1611.00278 · doi:10.1007/s00010-023-00943-4
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.
to appear in Aequationes Mathematicae