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)

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [685], line 19
     17 E = EllipticCurve(K, (a, b))
     18 G = E(Integer(0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798), Integer(0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8))
---> 19 E.set_order(Integer(0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141) * Integer(0x1))

File /private/var/tmp/sage-9.8-current/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/sage/schemes/elliptic_curves/ell_finite_field.py:1302, in EllipticCurve_finite_field.set_order(self, value, check, num_checks)
   1300 a,b = Hasse_bounds(q,1)
   1301 if not a <= value <= b:
-> 1302     raise ValueError('Value %s illegal (not an integer in the Hasse range)' % value)
   1303 # Is value*random == identity?
   1304 for i in range(num_checks):

ValueError: Value 115792089237316195423570985008687907852837564279074904382605163141518161494337 illegal (not an integer in the Hasse range)

We can convert even to (p ^ 2) for secp256k1 but this is useless because we cannot do twist/subgroup/invalid curve attack.

The question is: does it mean that there is some kind of connection between y^2=x^3+7, and for example y^2=x^3+2? Or maybe there is another connection, where points on curves with identical p-value and n-value can be mapped? Does it mean, that if we have b=0x7, where there are "n" points, and for example b=0xc curve also has the same amount of points, then does it mean we can map them 1:1?

The question is: does it mean that there is some kind of connection between y^2=x^3+7, and for example y^2=x^3+2? Or maybe there is another connection, where points on curves with identical p-value and n-value can be mapped? Does it mean, that if we have b=0x7, where there are "n" points, and for example b=0xc curve also has the same amount of points, then does it mean we can map them 1:1?