Elkies maintains [a list of nontorsion points of low height on elliptic curves over Q](http://www.math.harvard.edu/~elkies/low_height.html); does anyone know of anything similar for curves over number fields?

Everest and Ward [give examples](https://ueaeprints.uea.ac.uk/19694/) of points of height 0.01032... and 0.009721... on curves over Q(w) for w a cube root of unity or the golden ratio respectively. I have made a modest improvement in the latter case, recovering a point of height 0.009128... . 

In the context of the elliptic Lehmer problem the aim is to minimise dh(P) for d the degree of the number field, so working over quadratic extensions a point would have to have height less than 0.005 to be competitive with the examples in Elkies' table. Are there any examples?