Title: Real elliptic curves and cevian geometry,
Abstract: We study the elliptic curve $E_a: (ax+1)y^2+(ax+1)(x-1)y+x^2-x=0$, which we
call the geometric normal form of an elliptic curve. We show that any elliptic
curve whose $j$-invariant is real is isomorphic to a curve $E_a$ in geometric
normal form, and show that for $a \notin \{0, -1, -9\}$, the points on $E_a$,
minus a set of $6$ points, can be characterized in terms of the cevian geometry
of a triangle.