Quadratic Twist Point Equiv galois

theorem quadraticTwistPointEquiv_galois (σ : M ≃ₐ[K] M) (P : ((E.quadraticTwist L)⁄M).Point) :    E.quadraticTwistPointEquiv L M (Affine.Point.map σ.toAlgHom P) =      (quadraticCharacter K L M σ : ℤ) •        Affine.Point.map σ.toAlgHom (E.quadraticTwistPointEquiv L M P) := by  by_cases hσ : ∀ x : L, σ (algebraMap L M x) = algebraMap L M x  · -- `σ` fixes `L` pointwise (`χ(σ) = 1`): this is naturality for the `L`-algebra map behind `σ`.    rw [(quadraticCharacter_eq_one_iff K L M σ).mpr hσ, Units.val_one, one_zsmul]    exact E.quadraticTwistPointEquiv_map L M ({ σ.toAlgHom with commutes' := hσ } : M →ₐ[L] M) P  · -- `σ` moves `L` (`χ(σ) = -1`): anti-equivariance.    have hχ : quadraticCharacter K L M σ = -1 :=      (Int.units_eq_one_or _).resolve_left        fun h ↦ hσ ((quadraticCharacter_eq_one_iff K L M σ).mp h)    rw [hχ, Units.val_neg, Units.val_one, neg_one_zsmul]    exact E.quadraticTwistPointEquiv_map_of_not_fixed L M hσ P