diff --git a/ivc/src/ivc/mod.rs b/ivc/src/ivc/mod.rs
index ff00aaa1df..4dbd8e7f84 100644
--- a/ivc/src/ivc/mod.rs
+++ b/ivc/src/ivc/mod.rs
@@ -10,8 +10,16 @@ pub const LIMB_BITSIZE_XLARGE: usize = 150;
 /// The biggest packing format, 2 limbs.
 pub const N_LIMBS_XLARGE: usize = 2;
 
+/// Number of additional columns that a reduction to degree 2 will
+/// require.
+// This value has been generated using a fake folding config like in
+// [folding::tests::test_quadraticization]
+pub const N_ADDITIONAL_WIT_COL_QUAD: usize = 48;
+
 #[cfg(test)]
 mod tests {
+    use std::collections::HashMap;
+
     use crate::{
         ivc::{
             columns::{IVCColumn, IVC_NB_TOTAL_FIXED_SELECTORS, N_BLOCKS},
@@ -20,7 +28,10 @@ mod tests {
             lookups::IVCLookupTable,
         },
         poseidon_8_56_5_3_2::{
-            bn254::{PoseidonBN254Parameters, STATE_SIZE as IVC_POSEIDON_STATE_SIZE},
+            bn254::{
+                PoseidonBN254Parameters, NB_CONSTRAINTS as IVC_POSEIDON_NB_CONSTRAINTS,
+                STATE_SIZE as IVC_POSEIDON_STATE_SIZE,
+            },
             interpreter::PoseidonParams,
         },
     };
@@ -39,8 +50,13 @@ mod tests {
 
     // Total number of columns in IVC and Application circuits.
     pub const TEST_N_COL_TOTAL: usize = IVCColumn::N_COL + 50;
-    // Absolutely no idea.
-    pub const TEST_N_CHALS: usize = 200;
+
+    // Number of challenges in the IVC circuit.
+    // It is the maximum number of constraints per row.
+    // We do suppose it is Poseidon which has the highest number of constraints
+    // for now.
+    pub const TEST_N_CHALS: usize = IVC_POSEIDON_NB_CONSTRAINTS;
+
     pub const TEST_DOMAIN_SIZE: usize = 1 << 15;
 
     type IVCWitnessBuilderEnvRaw<LT> = WitnessBuilderEnv<
@@ -134,6 +150,30 @@ mod tests {
         );
     }
 
+    #[test]
+    fn test_regression_ivc_constraints() {
+        let mut constraint_env = ConstraintBuilderEnv::<Fp, IVCLookupTable<Ff1>>::create();
+        constrain_ivc::<Fp, Ff1, _>(&mut constraint_env);
+        let constraints = constraint_env.get_relation_constraints();
+
+        let mut constraints_degrees = HashMap::new();
+
+        // Regression testing for the number of constraints and their degree
+        {
+            // Hashes are not included for now.
+            assert_eq!(constraints.len(), 55);
+            constraints.iter().for_each(|c| {
+                let degree = c.degree(1, 0);
+                *constraints_degrees.entry(degree).or_insert(0) += 1;
+            });
+
+            assert_eq!(constraints_degrees.get(&1), None);
+            assert_eq!(constraints_degrees.get(&2), Some(&29));
+            assert_eq!(constraints_degrees.get(&3), Some(&5));
+            assert_eq!(constraints_degrees.get(&4), Some(&21));
+        }
+    }
+
     #[test]
     fn test_completeness_ivc() {
         let mut rng = o1_utils::tests::make_test_rng(None);