Question about Novotney's paper on Weak Curves
There is obviously missing information on both lecture projects. With a small try, I've found a curve with the required order.
If you set the field as the prime field $F_P$ where $p=9254331510119$, the curve
$$E(F_p) : y^2 = x^3 + 7x + 1$$
p = 9254331510119
E = EllipticCurve(GF(p), [7,1])
print(E.order().factor())

outputs
$$9254332285624 = 2^3 \cdot 19 \cdot 23 \cdot 67 \cdot 2089 \cdot 18913$$ as required.

Actually, I was lucky since I simply started 9254332285624-1000000  and I did not use the Hasse bound
$$|N - (q+1)| \le 2 \sqrt{q}$$ where $N$ is the number of point on the curve, here $N= 9254332285624$, and $q$ is the number of elements of the finite field, here we have the prime field $F_p$. With removing the absolute value we have this form
$$q+1-2{\sqrt q} ≤ N ≤ q+1+2{\sqrt q}$$
$$q+1-2{\sqrt q} ≤ 9254332285624 ≤ q+1+2{\sqrt q}$$
and calculating
$$9254332285625 - 4 \sqrt{2313583071406} \leq q \leq 9254332285625 + 4 \sqrt{2313583071406} $$
$$9254326201438 &lt; q &lt; 9254338369812$$
So, if you seek the primes in the above range ( possibly with a next_prime function of SageMath) you will definitely find your candidate primes, which are expected little ( exactly 407391 primes on this range) to satisfy the required curve order.

The SageMath code with Hasse Bound;
expected_order = 2^3 * 19 * 23 * 67 * 2089 * 18913

#This is specific to this order!
start = floor(expected_order - 4 * sqrt(expected_order/4))
end   = floor(expected_order + 4 * sqrt(expected_order/4))

p = start -1

primeCount = 0

for x  in range(start,end):
    p = p.next_prime()
    primeCount = primeCount + 1
    if p &gt; end:
        break
        
    E = EllipticCurve(GF(p), [7,1])
    
    if E.order() == expected_order:
        print ( p)
        break
    
print(&quot;Finished&quot;)
print(&quot;Number of tested primes =&quot;, primeCount)

and the output;
9254331510119
Finished
Number of tested primes = 177222