Neuberg cubics over finite fields

Details Neuberg cubics over finite fields Neuberg cubics over finite fields

2008-06-16

arxiv.org/abs/0806.2495v1

Mathematics

Algebraic Geometry

16 pages, 6 figures

Scientific paper

The framework of universal geometry allows us to consider metrical properties of affine views of elliptic curves, even over finite fields. We show how the Neuberg cubic of triangle geometry extends to the finite field situation and provides interesting potential invariants for elliptic curves, focussing on an explicit example over $\mathbb{F}_{23}$. We also prove that tangent conics for a Weierstrass cubic are identical or disjoint.

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