Steve Trettel · with Nadir Hajouji

elliptic 7 2 · 2025

The elliptic curve $y^2=x^3+5x+7$ mod 11, over the field with 121 elements.

An elliptic curve on a torus with lattice parameter $\tau = \frac{1}{2} + \frac{\sqrt{7}}{2}i$ (discriminant $D = 7$ ) is lifted to $S^3$ via the Hopf fibration and stereographically projected to $\mathbb{R}^3$ . The curve is defined by a degree-7 perturbation: $\phi(t) = \frac{\pi}{2} + \epsilon a \cos(7t)$ , $\theta(t) = t + \epsilon \sin(14t)$ , producing a surface with 7-fold near-symmetry. Rendered with a GPU pathtracer. Controls: Click and drag to orbit, scroll to zoom.

Steve Trettel · with Nadir Hajouji

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