ark-curves-cherry-picked/ed_on_mnt4_753/scripts/scalar_field.sage

modulus = 5237311370989869175293026848905079641021338739994243633972937865128169101571388346632361720473792365177258871486054600656048925740061347509722287043067341250552640264308621296888446513816907173362124418513727200975392177480577

assert(modulus.is_prime())

Fp = GF(modulus)

generator = Fp(0);
for i in range(0, 20):
    i = Fp(i);
    neg_i = Fp(-i)
    if not(i.is_primitive_root() or neg_i.is_primitive_root()):
        continue
    elif i.is_primitive_root():
        assert(i.is_primitive_root());
        print("Generator: %d" % i)
        generator = i
        break
    else:
        assert(neg_i.is_primitive_root());
        print("Generator: %d" % neg_i)
        generator = neg_i
        break


two_adicity = valuation(modulus - 1, 2);
trace = (modulus - 1) / 2**two_adicity;
two_adic_root_of_unity = generator^trace
print("2-adic Root of Unity: %d " % two_adic_root_of_unity)