Signed norm curves in odd field degree have no bad reduction primes. Their integral point count has no logarithmic loss, as required by the odd-degree branch of CCDN Theorem 6.

theorem CCDN.signed_norm_curve_log_free_count (K : Type u_1) [Field K] [NumberField K] (β : NumberField.RingOfIntegers K) {ε : ℤ} (hε : IsUnit ε) (hn : 2 ≤ Module.finrank ℚ K) (hodd : Odd (Module.finrank ℚ K)) {B : ℝ} (hB : 1 ≤ B) : ↑(count (zeroLocus ((MvPolynomial.map (Int.castRingHom ℚ)) (signedNormCurvePolynomial K β ε))) B) ≤ 3 * affineHypersurfaceAuxiliaryConstant 0 * ↑(Module.finrank ℚ K) ^ 4 * B ^ (1 / ↑(Module.finrank ℚ K))

The constant is absolute and the degree dependence polynomial. The sign can be either unit of the integers, and the generator is arbitrary.