We provide a complete classification of well-rounded ideal lattices arising from real quadratic fields. We show that the ideals that give rise to such lattices are precisely the ones that correspond to divisors $a$ of the discriminant $d$ that satisfy $\sqrt{\frac{d}{3}}<a<\sqrt{3d}.$
Non-existence of elliptic curves with everywhere good reduction over some real quadratic fields
Simultaneous indivisibility of class numbers of pairs of real quadratic fields
Class number one problem for the real quadratic fields $\mathbb{Q}({\sqrt{m^2+2r}})$
![QR code for arXiv:1902.01773 [math.NT]](http://oss.arxitics.com/images/favicon.svg)