Let E be an elliptic curve defined over Q given by an affine Weierstrass equation of the form (1) E : y = x + ax + b (a, b ∈ Z, x, y ∈ Q). Reducing the elliptic curve (1) modulo a sufficiently large prime p, we obtain an elliptic curve Ẽp over Fp. Considering an infinite sequence of elliptic curves Ẽp, we map the point (x, y) of them into the unit square [0, 1) via the mapping (x, y) 7→ ( x p ,...