We can convert even to (p ^ 2) for secp256k1 but this is useless because we cannot do twist/subgroup/invalid curve attack.
Could you please explain what do you mean by p^2 exactly?
Yes we can increase p parameter of secp256k1 to do invalid/twist attack but we got infinity point and if you will factorize that prime you will see all factored primes
p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f ** 2
K = GF(p)
a = K(0x0000000000000000000000000000000000000000000000000000000000000000)
b = K(0x0000000000000000000000000000000000000000000000000000000000000007)
E = EllipticCurve(K, (a, b))
G = E(0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798, 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8)
E.set_order(0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141 * 0x1)