diff --git a/arrabiata/src/constraints.rs b/arrabiata/src/constraints.rs
index d568fd6699..1bc542a4ca 100644
--- a/arrabiata/src/constraints.rs
+++ b/arrabiata/src/constraints.rs
@@ -5,6 +5,8 @@ use crate::{
     interpreter::{self, Instruction, Side},
     MAX_DEGREE, NUMBER_OF_COLUMNS, NUMBER_OF_PUBLIC_INPUTS,
 };
+use ark_ec::{short_weierstrass::SWCurveConfig, CurveConfig};
+use ark_ff::PrimeField;
 use kimchi::circuits::{
     expr::{ConstantTerm::Literal, Expr, ExprInner, Operations, Variable},
     gate::CurrOrNext,
@@ -12,12 +14,12 @@ use kimchi::circuits::{
 use log::debug;
 use num_bigint::BigInt;
 use o1_utils::FieldHelpers;
+use poly_commitment::commitment::CommitmentCurve;
 
 #[derive(Clone, Debug)]
 pub struct Env<C: ArrabiataCurve> {
     /// The parameter a is the coefficients of the elliptic curve in affine
     /// coordinates.
-    // FIXME: this is ugly. Let use the curve as a parameter. Only lazy for now.
     pub a: BigInt,
     pub idx_var: usize,
     pub idx_var_next_row: usize,
@@ -26,9 +28,13 @@ pub struct Env<C: ArrabiataCurve> {
     pub activated_gadget: Option<Gadget>,
 }
 
-impl<C: ArrabiataCurve> Env<C> {
-    pub fn new(a: BigInt) -> Self {
+impl<C: ArrabiataCurve> Env<C>
+where
+    <<C as CommitmentCurve>::Params as CurveConfig>::BaseField: PrimeField,
+{
+    pub fn new() -> Self {
         // This check might not be useful
+        let a: BigInt = <C as CommitmentCurve>::Params::COEFF_A.to_biguint().into();
         assert!(
             a < C::ScalarField::modulus_biguint().into(),
             "a is too large"
@@ -371,3 +377,12 @@ impl<C: ArrabiataCurve> Env<C> {
         constraints
     }
 }
+
+impl<C: ArrabiataCurve> Default for Env<C>
+where
+    <<C as CommitmentCurve>::Params as CurveConfig>::BaseField: PrimeField,
+{
+    fn default() -> Self {
+        Self::new()
+    }
+}
diff --git a/arrabiata/tests/constraints.rs b/arrabiata/tests/constraints.rs
index 72899b059a..abc523efa3 100644
--- a/arrabiata/tests/constraints.rs
+++ b/arrabiata/tests/constraints.rs
@@ -7,22 +7,21 @@ use arrabiata::{
 };
 use mina_curves::pasta::{curves::vesta::Vesta, fields::Fp, Pallas};
 use mvpoly::{monomials::Sparse, MVPoly};
-use num_bigint::BigInt;
 use std::collections::HashMap;
 
 fn helper_compute_constraints_gadget(instr: Instruction, exp_constraints: usize) {
-    let mut constraints_fp = constraints::Env::<Vesta>::new(BigInt::from(0_usize));
+    let mut constraints_fp = constraints::Env::<Vesta>::new();
 
     interpreter::run_ivc(&mut constraints_fp, instr);
     assert_eq!(constraints_fp.constraints.len(), exp_constraints);
 
-    let mut constraints_fq = constraints::Env::<Pallas>::new(BigInt::from(0_usize));
+    let mut constraints_fq = constraints::Env::<Pallas>::new();
     interpreter::run_ivc(&mut constraints_fq, instr);
     assert_eq!(constraints_fq.constraints.len(), exp_constraints);
 }
 
 fn helper_check_expected_degree_constraints(instr: Instruction, exp_degrees: HashMap<u64, usize>) {
-    let mut constraints_fp = constraints::Env::<Vesta>::new(BigInt::from(0_usize));
+    let mut constraints_fp = constraints::Env::<Vesta>::new();
     interpreter::run_ivc(&mut constraints_fp, instr);
 
     let mut actual_degrees: HashMap<u64, usize> = HashMap::new();
@@ -51,7 +50,7 @@ fn helper_gadget_number_of_columns_used(
     exp_nb_columns: usize,
     exp_nb_public_input: usize,
 ) {
-    let mut constraints_fp = constraints::Env::<Vesta>::new(BigInt::from(0_usize));
+    let mut constraints_fp = constraints::Env::<Vesta>::new();
     interpreter::run_ivc(&mut constraints_fp, instr);
 
     let nb_columns = constraints_fp.idx_var;
@@ -62,7 +61,7 @@ fn helper_gadget_number_of_columns_used(
 }
 
 fn helper_check_gadget_activated(instr: Instruction, gadget: Gadget) {
-    let mut constraints_fp = constraints::Env::<Vesta>::new(BigInt::from(0_usize));
+    let mut constraints_fp = constraints::Env::<Vesta>::new();
     interpreter::run_ivc(&mut constraints_fp, instr);
 
     assert_eq!(constraints_fp.activated_gadget, Some(gadget));
@@ -103,7 +102,7 @@ fn test_gadget_elliptic_curve_addition() {
 
 #[test]
 fn test_ivc_total_number_of_constraints_ivc() {
-    let constraints_fp = constraints::Env::<Vesta>::new(BigInt::from(0_usize));
+    let constraints_fp = constraints::Env::<Vesta>::new();
 
     let constraints = constraints_fp.get_all_constraints_for_ivc();
     assert_eq!(constraints.len(), 28);
@@ -111,7 +110,7 @@ fn test_ivc_total_number_of_constraints_ivc() {
 
 #[test]
 fn test_degree_of_constraints_ivc() {
-    let constraints_fp = constraints::Env::<Vesta>::new(BigInt::from(0_usize));
+    let constraints_fp = constraints::Env::<Vesta>::new();
 
     let constraints = constraints_fp.get_all_constraints_for_ivc();
 
@@ -149,7 +148,7 @@ fn test_gadget_elliptic_curve_scaling() {
 // It doesn't test anything in particular. It is mostly an "integration" test.
 #[test]
 fn test_integration_with_mvpoly_to_compute_cross_terms() {
-    let constraints_fp = constraints::Env::<Vesta>::new(BigInt::from(0_usize));
+    let constraints_fp = constraints::Env::<Vesta>::new();
 
     let constraints = constraints_fp.get_all_constraints_for_ivc();
     let mut rng = o1_utils::tests::make_test_rng(None);