|Information from Kimberling's Encyclopedia of Triangle Centers|
Trilinears a/(AB - AC) : b/(BC - BA) : c/(CA -CB)
Barycentrics a2/(AB - AC) : b2/(BC - BA) : c2/(CA -CB)
The Hofstadter ellipse E(0) is described at X(359). The point other than A, B, and C in which E(0) meets the circumcircle is X(3067). As with X(359) and X(360), this is a transcendental center, with "exposed angles" A, B, C in its coordinates.