How to check if a point is generator in an elliptic curve?

[erhant]

In cyclic groups, I could use co-factor clearing to check if a point is a generator:

def find_generators(p):
  Fp = GF(p)

  order = p - 1
  factorization = factor(order)
  print("Factors of", order, "are", factorization)

  gens = []
  for e in range(2, p):
    e = Fp(e)

    is_gen = True
    for f in map(lambda f: f[0], factorization):
      cf = order // f # cofactor
      if e ** cf == 1:
        # cofactor clearing results in 1, this is NOT a generator
        is_gen = False
        break

    if is_gen:
      gens.append(e)

  print(gens)
  assert(len(gens) == euler_phi(order))

Is there something analogous to this one for Elliptic Curves?

[skaunov]

I could be wrong, but I feel like the same should work for EC too, since we just check if the group operation applied subgroup order times to e yields identity element.

So I'd just take EC order for order and scalar multiplication instead of power.

[skaunov]

So...
In https://github.com/LeastAuthority/moonmath-manual/blob/158934a9e4452ae127dae0814fb43be2816cd9c1/chapters/algebra-moonmath.tex#L211 cofactor clearing is described in relation to finite cyclic groups (and not restricted to multiplicative groups of integers modulo a prime). (And details are outlined in the definition in the beginning of the subsection.)
Next, it's stated that "It can be shown that this group is finite and cyclic whenever the underlying field $\F$ is finite.", consequently cofactor clearing should be applicable to EC as well. Cheers!