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arXiv · 1711.11415

Real elliptic curves and cevian geometry

Igor Minevich·Patrick Morton
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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.

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Igor Minevich, Patrick Morton. 2017-11-25. Real elliptic curves and cevian geometry. https://arxiv.org/abs/1711.11415

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