diff --git a/sage/gen_exhaustive_groups.sage b/sage/gen_exhaustive_groups.sage
index 3c3c984811e3a..01d15dcdeac56 100644
--- a/sage/gen_exhaustive_groups.sage
+++ b/sage/gen_exhaustive_groups.sage
@@ -1,9 +1,4 @@
-# Define field size and field
-P = 2^256 - 2^32 - 977
-F = GF(P)
-BETA = F(0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee)
-
-assert(BETA != F(1) and BETA^3 == F(1))
+load("secp256k1_params.sage")
 
 orders_done = set()
 results = {}
diff --git a/sage/secp256k1.sage b/sage/prove_group_implementations.sage
similarity index 100%
rename from sage/secp256k1.sage
rename to sage/prove_group_implementations.sage
diff --git a/sage/secp256k1_params.sage b/sage/secp256k1_params.sage
new file mode 100644
index 0000000000000..ad77f7b4e3975
--- /dev/null
+++ b/sage/secp256k1_params.sage
@@ -0,0 +1,32 @@
+"""Prime order of finite field underlying secp256k1 (2^256 - 2^32 - 977)"""
+P = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
+
+"""Finite field underlying secp256k1"""
+F = FiniteField(P)
+
+"""Elliptic curve secp256k1: y^2 = x^3 + 7"""
+C = EllipticCurve([F(0), F(7)])
+
+"""Base point of secp256k1"""
+G = C.lift_x(0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798)
+
+"""Prime order of secp256k1"""
+N = C.order()
+
+"""Finite field of scalars of secp256k1"""
+Z = FiniteField(N)
+
+""" Beta value of secp256k1 non-trivial endomorphism: lambda * (x, y) = (beta * x, y)"""
+BETA = F(2)^((P-1)/3)
+
+""" Lambda value of secp256k1 non-trivial endomorphism: lambda * (x, y) = (beta * x, y)"""
+LAMBDA = Z(3)^((N-1)/3)
+
+assert is_prime(P)
+assert is_prime(N)
+
+assert BETA != F(1)
+assert BETA^3 == F(1)
+
+assert LAMBDA != Z(1)
+assert LAMBDA^3 == Z(1)