Function aut_1728 

pub fn aut_1728(p: &BigInt, pt: &Point2) -> Point2

The order-4 automorphism ι:(x,y) ↦ (−x, i·y) of the j = 1728 curve y² = x³ + x (i² = −1 lives in 𝔽_{p²} for p ≡ 3 mod 4). ι² = [−1], so ⟨ι⟩ ≅ ℤ/4 = Aut(E₀). It permutes the keyspace, and E₀/⟨K⟩ ≅ E₀/⟨ι(K)⟩ — the symmetry that makes recovering one kernel recover its whole orbit.