diff --git a/src/core/backend/avx512/quotients.rs b/src/core/backend/avx512/quotients.rs
index b13a3dc8a..4433acd4d 100644
--- a/src/core/backend/avx512/quotients.rs
+++ b/src/core/backend/avx512/quotients.rs
@@ -3,7 +3,7 @@ use itertools::zip_eq;
 use super::qm31::PackedQM31;
 use super::{AVX512Backend, VECS_LOG_SIZE};
 use crate::core::backend::avx512::PackedBaseField;
-use crate::core::backend::cpu::quotients::column_constants;
+use crate::core::backend::cpu::quotients::{quotient_constants, QuotientConstants};
 use crate::core::circle::CirclePoint;
 use crate::core::commitment_scheme::quotients::{ColumnSampleBatch, QuotientOps};
 use crate::core::fields::m31::BaseField;
@@ -23,7 +23,7 @@ impl QuotientOps for AVX512Backend {
     ) -> SecureEvaluation<Self> {
         assert!(domain.log_size() >= VECS_LOG_SIZE as u32);
         let mut values = SecureColumn::<AVX512Backend>::zeros(domain.size());
-        let column_constants = column_constants(sample_batches, random_coeff);
+        let quotient_constants = quotient_constants(sample_batches, random_coeff);
 
         // TODO(spapini): bit reverse iterator.
         for vec_row in 0..(1 << (domain.log_size() - VECS_LOG_SIZE as u32)) {
@@ -39,7 +39,7 @@ impl QuotientOps for AVX512Backend {
             let row_accumulator = accumulate_row_quotients(
                 sample_batches,
                 columns,
-                &column_constants,
+                &quotient_constants,
                 vec_row,
                 random_coeff,
                 (domain_points_x, domain_points_y),
@@ -53,13 +53,14 @@ impl QuotientOps for AVX512Backend {
 pub fn accumulate_row_quotients(
     sample_batches: &[ColumnSampleBatch],
     columns: &[&CircleEvaluation<AVX512Backend, BaseField, BitReversedOrder>],
-    column_constants: &[Vec<(SecureField, SecureField, SecureField)>],
+    quotient_constants: &QuotientConstants,
     vec_row: usize,
     random_coeff: SecureField,
     domain_point_vec: (PackedBaseField, PackedBaseField),
 ) -> PackedQM31 {
     let mut row_accumulator = PackedQM31::zero();
-    for (sample_batch, sample_constants) in zip_eq(sample_batches, column_constants) {
+    for (sample_batch, sample_constants) in zip_eq(sample_batches, &quotient_constants.line_coeffs)
+    {
         let mut numerator = PackedQM31::zero();
         for ((column_index, _), (a, b, c)) in
             zip_eq(&sample_batch.columns_and_values, sample_constants)
diff --git a/src/core/backend/cpu/quotients.rs b/src/core/backend/cpu/quotients.rs
index f8266c3cd..453e560dd 100644
--- a/src/core/backend/cpu/quotients.rs
+++ b/src/core/backend/cpu/quotients.rs
@@ -4,7 +4,7 @@ use num_traits::{One, Zero};
 use super::CPUBackend;
 use crate::core::circle::CirclePoint;
 use crate::core::commitment_scheme::quotients::{ColumnSampleBatch, PointSample, QuotientOps};
-use crate::core::constraints::{complex_conjugate_line_coefficients, pair_vanishing};
+use crate::core::constraints::{complex_conjugate_line_coeffs, pair_vanishing};
 use crate::core::fields::m31::BaseField;
 use crate::core::fields::qm31::SecureField;
 use crate::core::fields::secure_column::SecureColumn;
@@ -21,7 +21,7 @@ impl QuotientOps for CPUBackend {
         sample_batches: &[ColumnSampleBatch],
     ) -> SecureEvaluation<Self> {
         let mut values = SecureColumn::zeros(domain.size());
-        let column_constants = column_constants(sample_batches, random_coeff);
+        let quotient_constants = quotient_constants(sample_batches, random_coeff);
 
         for row in 0..domain.size() {
             // TODO(alonh): Make an efficient bit reverse domain iterator, possibly for AVX backend.
@@ -29,7 +29,7 @@ impl QuotientOps for CPUBackend {
             let row_value = accumulate_row_quotients(
                 sample_batches,
                 columns,
-                &column_constants,
+                &quotient_constants,
                 row,
                 random_coeff,
                 domain_point,
@@ -43,13 +43,14 @@ impl QuotientOps for CPUBackend {
 pub fn accumulate_row_quotients(
     sample_batches: &[ColumnSampleBatch],
     columns: &[&CircleEvaluation<CPUBackend, BaseField, BitReversedOrder>],
-    column_constants: &[Vec<(SecureField, SecureField, SecureField)>],
+    quotient_constants: &QuotientConstants,
     row: usize,
     random_coeff: SecureField,
     domain_point: CirclePoint<BaseField>,
 ) -> SecureField {
     let mut row_accumulator = SecureField::zero();
-    for (sample_batch, sample_constants) in zip_eq(sample_batches, column_constants) {
+    for (sample_batch, sample_constants) in zip_eq(sample_batches, &quotient_constants.line_coeffs)
+    {
         let mut numerator = SecureField::zero();
         for ((column_index, _), (a, b, c)) in
             zip_eq(&sample_batch.columns_and_values, sample_constants)
@@ -73,10 +74,11 @@ pub fn accumulate_row_quotients(
     row_accumulator
 }
 
-/// Precompute the complex conjugate line constants for each column in each sample batch.
+/// Precompute the complex conjugate line coefficients for each column in each sample batch.
 /// Specifically, for the i-th (in a sample batch) column's numerator term
-/// `alpha^i * (F(p) - (a * p.y + b))`, we precompute the constants `alpha^i * a` and alpha^i * `b`.
-pub fn column_constants(
+/// `alpha^i * (c * F(p) - (a * p.y + b))`, we precompute and return the constants:
+/// (`alpha^i * a`, `alpha^i * b`, `alpha^i * c`).
+pub fn column_line_coeffs(
     sample_batches: &[ColumnSampleBatch],
     random_coeff: SecureField,
 ) -> Vec<Vec<(SecureField, SecureField, SecureField)>> {
@@ -93,13 +95,28 @@ pub fn column_constants(
                         point: sample_batch.point,
                         value: *sampled_value,
                     };
-                    complex_conjugate_line_coefficients(&sample, alpha)
+                    complex_conjugate_line_coeffs(&sample, alpha)
                 })
                 .collect()
         })
         .collect()
 }
 
+pub fn quotient_constants(
+    sample_batches: &[ColumnSampleBatch],
+    random_coeff: SecureField,
+) -> QuotientConstants {
+    let line_coeffs = column_line_coeffs(sample_batches, random_coeff);
+    QuotientConstants { line_coeffs }
+}
+
+/// Holds the precomputed constant values used in each quotient evaluation.
+pub struct QuotientConstants {
+    /// The line coefficients for each quotient numerator term. For more details see
+    /// [self::column_line_coeffs].
+    pub line_coeffs: Vec<Vec<(SecureField, SecureField, SecureField)>>,
+}
+
 #[cfg(test)]
 mod tests {
     use crate::core::backend::cpu::{CPUCircleEvaluation, CPUCirclePoly};
diff --git a/src/core/commitment_scheme/quotients.rs b/src/core/commitment_scheme/quotients.rs
index 8cc8386b9..7c84204ed 100644
--- a/src/core/commitment_scheme/quotients.rs
+++ b/src/core/commitment_scheme/quotients.rs
@@ -4,7 +4,7 @@ use std::iter::zip;
 
 use itertools::{izip, multiunzip, Itertools};
 
-use crate::core::backend::cpu::quotients::{accumulate_row_quotients, column_constants};
+use crate::core::backend::cpu::quotients::{accumulate_row_quotients, quotient_constants};
 use crate::core::circle::CirclePoint;
 use crate::core::fields::m31::BaseField;
 use crate::core::fields::qm31::SecureField;
@@ -124,7 +124,7 @@ pub fn fri_answers_for_log_size(
 ) -> Result<SparseCircleEvaluation<SecureField>, VerificationError> {
     let commitment_domain = CanonicCoset::new(log_size).circle_domain();
     let sample_batches = ColumnSampleBatch::new_vec(samples);
-    let column_constants = column_constants(&sample_batches, random_coeff);
+    let quotient_constants = quotient_constants(&sample_batches, random_coeff);
     for queried_values in queried_values_per_column {
         if queried_values.len() != query_domain.flatten().len() {
             return Err(VerificationError::InvalidStructure(
@@ -155,7 +155,7 @@ pub fn fri_answers_for_log_size(
             let value = accumulate_row_quotients(
                 &sample_batches,
                 &column_evals.iter().collect_vec(),
-                &column_constants,
+                &quotient_constants,
                 row,
                 random_coeff,
                 domain_point,
diff --git a/src/core/constraints.rs b/src/core/constraints.rs
index 5631788e5..872c0cf1f 100644
--- a/src/core/constraints.rs
+++ b/src/core/constraints.rs
@@ -95,7 +95,7 @@ pub fn complex_conjugate_line(
 /// (conj(sample.y), conj(sample.value)).
 /// Relies on the fact that every polynomial F over the base
 /// field holds: F(p*) == F(p)* (* being the complex conjugate).
-pub fn complex_conjugate_line_coefficients(
+pub fn complex_conjugate_line_coeffs(
     sample: &PointSample,
     alpha: SecureField,
 ) -> (SecureField, SecureField, SecureField) {