Exists smul quadratic Twist base Change eq

theorem exists_smul_quadraticTwist_baseChange_eq :    ∃ C : VariableChange L, C • (E.quadraticTwist L).baseChange L = E.baseChange L := by  obtain ⟨σ, hσ⟩ := exists_algEquiv_ne_one K L  obtain ⟨θ, hθ⟩ := exists_notMem_range_algebraMap K L  obtain ⟨C₁, hC₁, -⟩ := E.exists_smul_baseChange_and_map_eq L hθ hσ  -- Bridge the chosen generator in `quadraticTwist L` to `θ`, base changed to `L`.  obtain ⟨C₀, hC₀⟩ := E.exists_smul_quadraticTwist_eq_quadraticTwistBy L hθ  exact ⟨C₁ * C₀.baseChange L, by rw [mul_smul, baseChange_smul_baseChange, hC₀, hC₁]⟩