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Can I quickly check the cofactor of secp256k1 is 1

I was wondering if there was a quick way to check that the group underlying the elliptic curve secp256k1 was indeed cyclic with the usual point G a generator. I am given the prime number underlying the field Fp, I am given the point G, I am given the integer orderwhich is presented as the order of the curve. I can check that the scalar multiplication order.G yields the infinity point. So I know that the order of G (i.e. the cardinal of its generated subgroup) divides order. I can check that order is a probable prime. So I reach the conclusion that the order of G is indeed order. But how do I know its generated subgroup is the whole elliptic curve?

import java.math.BigInteger; import org.bitcoinj.core.ECKey; import org.spongycastle.math.ec.ECCurve; import org.spongycastle.math.ec.ECPoint;   public class Test {   public static void main(String[] args){    // secp256k1 elliptic curve   ECCurve curve = ECKey.CURVE.getCurve();    // the order of the curve   BigInteger order = curve.getOrder();    // fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141   System.out.println(order.toString(16));    // The generator of the curve   ECPoint G = ECKey.CURVE.getG();   BigInteger X = G.getAffineXCoord().toBigInteger();   BigInteger Y = G.getAffineYCoord().toBigInteger();    // 79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798   System.out.println(X.toString(16));    // 483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8   System.out.println(Y.toString(16));     // Computing scalar multiplication order.G   ECPoint test = G.multiply(order);    System.out.println(test.isInfinity());  // true    // so we know the order of G (i.e. the cardinal of its   // generated subgroup) divides 'order'. However:    System.out.println(order.isProbablePrime(128)); // true    // and G is not infinity. So the order of G is precisely order.   // How do I check that the subgroup generated by G is actually    // the whole elliptic curve group, i.e. that the cofactor is 1?   } } 

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