diff --git a/src/bn256/fq.rs b/src/bn256/fq.rs
index f9c2e692..35714424 100644
--- a/src/bn256/fq.rs
+++ b/src/bn256/fq.rs
@@ -291,6 +291,7 @@ mod test {
     crate::field_testing_suite!(Fq, "quadratic_residue");
     crate::field_testing_suite!(Fq, "bits");
     crate::field_testing_suite!(Fq, "serialization_check");
+    crate::field_testing_suite!(Fq, "constants", MODULUS_STR);
 
     use crate::ff_ext::Legendre;
     use rand_core::OsRng;
diff --git a/src/bn256/fq2.rs b/src/bn256/fq2.rs
index 0ffc2514..a116f2fd 100644
--- a/src/bn256/fq2.rs
+++ b/src/bn256/fq2.rs
@@ -418,6 +418,7 @@ impl From<u64> for Fq2 {
     }
 }
 
+// This trait is only implemented to satisfy the requirement of CurveExt
 impl PrimeField for Fq2 {
     type Repr = Fq2Bytes;
 
diff --git a/src/bn256/fr.rs b/src/bn256/fr.rs
index c9776be9..28f8c476 100644
--- a/src/bn256/fr.rs
+++ b/src/bn256/fr.rs
@@ -339,6 +339,7 @@ mod test {
     crate::field_testing_suite!(Fr, "quadratic_residue");
     crate::field_testing_suite!(Fr, "bits");
     crate::field_testing_suite!(Fr, "serialization_check");
+    crate::field_testing_suite!(Fr, "constants", MODULUS_STR);
 
     use rand_core::OsRng;
 
@@ -360,12 +361,6 @@ mod test {
         }
     }
 
-    #[test]
-    fn test_delta() {
-        assert_eq!(Fr::DELTA, GENERATOR.pow([1u64 << Fr::S]));
-        assert_eq!(Fr::DELTA, Fr::MULTIPLICATIVE_GENERATOR.pow([1u64 << Fr::S]));
-    }
-
     #[test]
     fn test_from_u512() {
         assert_eq!(
diff --git a/src/pluto_eris/fields/fp.rs b/src/pluto_eris/fields/fp.rs
index 21d2541f..ec4b9ea9 100644
--- a/src/pluto_eris/fields/fp.rs
+++ b/src/pluto_eris/fields/fp.rs
@@ -408,6 +408,7 @@ mod test {
     crate::field_testing_suite!(Fp, "quadratic_residue");
     crate::field_testing_suite!(Fp, "bits");
     crate::field_testing_suite!(Fp, "serialization_check");
+    crate::field_testing_suite!(Fp, "constants", MODULUS_STR);
 
     use rand_core::OsRng;
 
@@ -429,12 +430,6 @@ mod test {
         }
     }
 
-    #[test]
-    fn test_delta() {
-        assert_eq!(Fp::DELTA, GENERATOR.pow([1u64 << Fp::S]));
-        assert_eq!(Fp::DELTA, Fp::MULTIPLICATIVE_GENERATOR.pow([1u64 << Fp::S]));
-    }
-
     #[test]
     fn test_zeta() {
         assert_eq!(Fp::ZETA * Fp::ZETA * Fp::ZETA, Fp::ONE);
diff --git a/src/pluto_eris/fields/fq.rs b/src/pluto_eris/fields/fq.rs
index 405c5188..e3d2b348 100644
--- a/src/pluto_eris/fields/fq.rs
+++ b/src/pluto_eris/fields/fq.rs
@@ -399,6 +399,7 @@ mod test {
     crate::field_testing_suite!(Fq, "quadratic_residue");
     crate::field_testing_suite!(Fq, "bits");
     crate::field_testing_suite!(Fq, "serialization_check");
+    crate::field_testing_suite!(Fq, "constants", MODULUS_STR);
 
     use rand_core::OsRng;
 
@@ -426,12 +427,6 @@ mod test {
         assert_ne!(Fq::ZETA * Fq::ZETA, Fq::ONE);
     }
 
-    #[test]
-    fn test_delta() {
-        assert_eq!(Fq::DELTA, GENERATOR.pow([1u64 << Fq::S]));
-        assert_eq!(Fq::DELTA, Fq::MULTIPLICATIVE_GENERATOR.pow([1u64 << Fq::S]));
-    }
-
     #[test]
     fn test_from_u512() {
         const N_VECS: usize = 10;
diff --git a/src/secp256k1/fp.rs b/src/secp256k1/fp.rs
index 65c3f42c..943addb4 100644
--- a/src/secp256k1/fp.rs
+++ b/src/secp256k1/fp.rs
@@ -299,6 +299,7 @@ mod test {
     crate::field_testing_suite!(Fp, "quadratic_residue");
     crate::field_testing_suite!(Fp, "bits");
     crate::field_testing_suite!(Fp, "serialization_check");
+    crate::field_testing_suite!(Fp, "constants", MODULUS_STR);
 
     use rand_core::OsRng;
 
@@ -320,29 +321,4 @@ mod test {
             assert!(a == b || a == negb);
         }
     }
-
-    #[test]
-    fn test_constants() {
-        assert_eq!(
-            Fp::MODULUS,
-            "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
-        );
-
-        assert_eq!(Fp::from(2) * Fp::TWO_INV, Fp::ONE);
-    }
-
-    #[test]
-    fn test_delta() {
-        assert_eq!(Fp::DELTA, MULTIPLICATIVE_GENERATOR.pow([1u64 << Fp::S]));
-    }
-
-    #[test]
-    fn test_root_of_unity() {
-        assert_eq!(Fp::ROOT_OF_UNITY.pow_vartime([1 << Fp::S]), Fp::one());
-    }
-
-    #[test]
-    fn test_inv_root_of_unity() {
-        assert_eq!(Fp::ROOT_OF_UNITY_INV, Fp::ROOT_OF_UNITY.invert().unwrap());
-    }
 }
diff --git a/src/secp256k1/fq.rs b/src/secp256k1/fq.rs
index 07863753..a6e19a75 100644
--- a/src/secp256k1/fq.rs
+++ b/src/secp256k1/fq.rs
@@ -306,6 +306,7 @@ mod test {
     crate::field_testing_suite!(Fq, "quadratic_residue");
     crate::field_testing_suite!(Fq, "bits");
     crate::field_testing_suite!(Fq, "serialization_check");
+    crate::field_testing_suite!(Fq, "constants", MODULUS_STR);
 
     use rand_core::OsRng;
 
@@ -327,29 +328,4 @@ mod test {
             assert!(a == b || a == negb);
         }
     }
-
-    #[test]
-    fn test_constants() {
-        assert_eq!(
-            Fq::MODULUS,
-            "0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141",
-        );
-
-        assert_eq!(Fq::from(2) * Fq::TWO_INV, Fq::ONE);
-    }
-
-    #[test]
-    fn test_delta() {
-        assert_eq!(Fq::DELTA, Fq::MULTIPLICATIVE_GENERATOR.pow([1u64 << Fq::S]));
-    }
-
-    #[test]
-    fn test_root_of_unity() {
-        assert_eq!(Fq::ROOT_OF_UNITY.pow_vartime([1 << Fq::S]), Fq::one());
-    }
-
-    #[test]
-    fn test_inv_root_of_unity() {
-        assert_eq!(Fq::ROOT_OF_UNITY_INV, Fq::ROOT_OF_UNITY.invert().unwrap());
-    }
 }
diff --git a/src/secp256r1/fp.rs b/src/secp256r1/fp.rs
index dcd2a021..098a12b1 100644
--- a/src/secp256r1/fp.rs
+++ b/src/secp256r1/fp.rs
@@ -317,6 +317,7 @@ mod test {
     crate::field_testing_suite!(Fp, "quadratic_residue");
     crate::field_testing_suite!(Fp, "bits");
     crate::field_testing_suite!(Fp, "serialization_check");
+    crate::field_testing_suite!(Fp, "constants", MODULUS_STR);
 
     use rand_core::OsRng;
 
@@ -338,29 +339,4 @@ mod test {
             assert!(a == b || a == negb);
         }
     }
-
-    #[test]
-    fn test_constants() {
-        assert_eq!(
-            Fp::MODULUS,
-            "0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff",
-        );
-
-        assert_eq!(Fp::from(2) * Fp::TWO_INV, Fp::ONE);
-    }
-
-    #[test]
-    fn test_delta() {
-        assert_eq!(Fp::DELTA, MULTIPLICATIVE_GENERATOR.pow([1u64 << Fp::S]));
-    }
-
-    #[test]
-    fn test_root_of_unity() {
-        assert_eq!(Fp::ROOT_OF_UNITY.pow_vartime([1 << Fp::S]), Fp::one());
-    }
-
-    #[test]
-    fn test_inv_root_of_unity() {
-        assert_eq!(Fp::ROOT_OF_UNITY_INV, Fp::ROOT_OF_UNITY.invert().unwrap());
-    }
 }
diff --git a/src/secp256r1/fq.rs b/src/secp256r1/fq.rs
index f4f94df4..6f7adbfa 100644
--- a/src/secp256r1/fq.rs
+++ b/src/secp256r1/fq.rs
@@ -306,6 +306,7 @@ mod test {
     crate::field_testing_suite!(Fq, "quadratic_residue");
     // crate::field_testing_suite!(Fq, "bits");
     crate::field_testing_suite!(Fq, "serialization_check");
+    crate::field_testing_suite!(Fq, "constants", MODULUS_STR);
 
     use rand_core::OsRng;
 
@@ -333,29 +334,4 @@ mod test {
             assert!(a == b || a == negb);
         }
     }
-
-    #[test]
-    fn test_constants() {
-        assert_eq!(
-            Fq::MODULUS,
-            "0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551",
-        );
-
-        assert_eq!(Fq::from(2) * Fq::TWO_INV, Fq::ONE);
-    }
-
-    #[test]
-    fn test_delta() {
-        assert_eq!(Fq::DELTA, Fq::MULTIPLICATIVE_GENERATOR.pow([1u64 << Fq::S]));
-    }
-
-    #[test]
-    fn test_root_of_unity() {
-        assert_eq!(Fq::ROOT_OF_UNITY.pow_vartime([1 << Fq::S]), Fq::one());
-    }
-
-    #[test]
-    fn test_inv_root_of_unity() {
-        assert_eq!(Fq::ROOT_OF_UNITY_INV, Fq::ROOT_OF_UNITY.invert().unwrap());
-    }
 }
diff --git a/src/tests/field.rs b/src/tests/field.rs
index 0073ad03..6b3c9479 100644
--- a/src/tests/field.rs
+++ b/src/tests/field.rs
@@ -439,4 +439,26 @@ macro_rules! field_testing_suite {
             end_timer!(start);
         }
     };
+
+    ($field: ident, "constants", $modulus_str: expr) => {
+        #[test]
+        fn test_primefield_constants() {
+            assert_eq!($field::MODULUS, $modulus_str);
+            assert_eq!(
+                $field::ROOT_OF_UNITY_INV,
+                $field::ROOT_OF_UNITY.invert().unwrap()
+            );
+            assert_eq!($field::from(2) * $field::TWO_INV, $field::ONE);
+            if $field::S != 0 {
+                assert_eq!(
+                    $field::ROOT_OF_UNITY.pow_vartime([1 << $field::S]),
+                    $field::one()
+                );
+                assert_eq!(
+                    $field::DELTA,
+                    $field::MULTIPLICATIVE_GENERATOR.pow([1u64 << $field::S])
+                );
+            }
+        }
+    };
 }