Elliptic curve point multiplication — who is wrong? I am relatively new to ECC, but my understanding is that the result of a point multiplication must still be a point on the curve. I have implemented an ECC calculator in Python, to add and multiply points on any curve mod p.

My misunderstanding is about the curve defined $y^2=x^3+2x+2 \pmod{17}$, with $\# E=19$. As $19$ is prime, Lagrange's theorem implies that all points except the point at infinity are generator points for the cyclic group. Considering the generator point $p=(5,1)$, my program says the result of $891p$ is $(6,14)$, while other online calculators say the result is $(11,3)$, but this point is not even on the curve!. Nearly always, both my own and online programs agree on the resultant point, but occasionally, like in this example, they do not.

Any help on this issue is appreciated, as to who is correct?
The (very useful!) computer algebra system sage says the correct result is indeed $(6,14)$:


sage: E = EllipticCurve(Zmod(17), [2, 2])
sage: E
Elliptic Curve defined by y^2 = x^3 + 2*x + 2 over Ring of integers modulo 17
sage: P = E(5, 1)
sage: 891 * P
(6 : 14 : 1)



Those "online calculators" you used appear to be broken.