Elliptic curve x^3 - y^2 = p

[cino hilliard <hillcino368@hotmail.com>]

Hi ,
I want to find the number of solutions of  the elliptic curve, x^3 - y^2 = p
for various p = 7, 431, 503, etc
 
I have been using brute force in a Pari script below testing for solutions.
 diffcubesq2(n,p) =
               {
               local(a,c=0,c2=0,j,k,y);
               for(j=1,n,
                for(k=1,n,
                 y=j^3-k^2;
                  if(y==p,
                   c++;
                   print(j","k","y);
                    );
                   );
                  );
                   c;
                   }

 diffcubesq2(10000,431) outputs
8,9,431
11,30,431
20,87,431
30,163,431
36,215,431
138,1621,431
150,1837,431
(03:14:10) gp > ##
  ***   last result computed in 6mn, 57,969 ms.
 
My Pari code misses the last two solutions. It would have
taken way too much time to get to y = 243836 anyway.  

>From a example and link posted by David Broadhurst in another forum,
 
http://magma.maths.usyd.edu.au/calc/
 
I tried using the Magma applet to compute the elliptic curve.
This gets all solutions in a fraction of the time.
 
Does anyone have Pari script with elliptic curve functions that will
do something like this?
 
 
Examples: p = 7 has 2 solutions, p = 431 has 9
Input:
E := EllipticCurve([0, -7]);
Q, reps := IntegralPoints(E);
Q;

Output:
Magma V2.15-3     Thu Jun 18 2009 17:24:22    [Seed = 2348296821]
   -------------------------------------
[ (2 : 1 : 1), (32 : -181 : 1) ]
Total time: 0.350 seconds, Total memory usage: 136.95MB

Input:
E := EllipticCurve([0, -431]);
Q, reps := IntegralPoints(E);
Q;
 
Output:
Magma V2.15-3     Thu Jun 18 2009 17:33:07    [Seed = 3601166652]
   -------------------------------------
[ (8 : 9 : 1), (20 : -87 : 1), (11 : -30 : 1), (30 : -163 : 1), (36 : 215 : 1),
(138 : 1621 : 1), (150 : 1837 : 1), (575 : 13788 : 1), (3903 : -243836 : 1) ]
Total time: 1.050 seconds, Total memory usage: 137.04MB

Thanks,
Cino