The elliptic curve $y^2=x^3+3$ mod 7, over the field with 343 elements, embedded in a characteristic zero curve with hexagonal symmetry.
An elliptic curve on a torus with lattice parameter τ=−21+23i (hexagonal lattice, discriminant D=3) is lifted to a surface in S3 via the Hopf fibration, then stereographically projected to R3. The curve on the torus is defined by a perturbation of a great circle: ϕ(t)=2π+ϵacos(3t), θ(t)=t+ϵsin(6t), giving a trefoil-like winding. Rational points from the elliptic curve are displayed as spheres on the surface, scaled by the conformal factor of stereographic projection. The scene is rendered with a GPU pathtracer.
Controls: Click and drag to orbit, scroll to zoom.
