question on inconsistent results for a curve and ellrank() command

[American Citizen <website.reader3@gmail.com>]

Hello:

See attached gp-pari file.

While running my programs I stumbled across an inconsistent results 
which caused me to take a careful look.

Here are those results involving a certain elliptic curve:

E = [0, 12304376939822994932659524, 0, 
-3648259547053109398533591982691229700073064038400, 0]

3 points of the 4 points Mordell-Weil basis (set) [ I had to do some 
work to finally settle down on these 3 points ]

p = [[-999779060917633308399360, 3866142351194747967608412122674782720], 
[-293883589543938115962240, 1452405131779215974552917691531685120], 
[-1406975789099557808651520, 5167717070222070579741742214157519360]]

I am trying to recover the 4th point right now.

However when I run the ellrank(E,{effort}) command, differing results 
come up.

> [0, 12304376939822994932659524, 0, 
> -3648259547053109398533591982691229700073064038400, 0]
> [[-999779060917633308399360, 3866142351194747967608412122674782720], 
> [-293883589543938115962240, 1452405131779215974552917691531685120], 
> [-1406975789099557808651520, 5167717070222070579741742214157519360]]
> e is a rank 4 curve with SHA > 1
> setting precision = 19
> ellrank(E)
> [0, 6, 0, []]
> ellrank(E,2)
> [2, 6, 0, [[-293883589543938115962240, 
> 1452405131779215974552917691531685120]]]
> ellrank(E,3)
> setting precision = 38
> ellrank(E)
> [0, 6, 0, []]
> ellrank(E,2)
> [2, 6, 0, [[-6105797019069920466053760, 
> 15917389406358134595823780451205131520], [-1910041765787625231041280, 
> 6699967211953306552674675136155240960]]]
> ellrank(E,3)
> setting precision = 57
> ellrank(E)
> [0, 6, 0, []]
> ellrank(E,2)
> [2, 6, 0, [[-2604689033065838647568640, 
> 8678086907094504656562057134370808320]]]
> ellrank(E,3)
> setting precision = 84
> ellrank(E)
> [0, 6, 0, []]
> ellrank(E,2)
> [2, 6, 0, [[482298396787552594734284800, 
> 10726073559724236251459173261972663500800]]]
> ellrank(E,3)
> setting precision = 96
> ellrank(E)
> [0, 6, 0, []]
> ellrank(E,2)
> [0, 6, 0, []]
> ellrank(E,3)
> setting precision = 115
> ellrank(E)
> [0, 6, 0, []]
> ellrank(E,2)
> [2, 6, 0, [[-1406975789099557808651520, 
> 5167717070222070579741742214157519360], [-999779060917633308399360, 
> 3866142351194747967608412122674782720]]]
> ellrank(E,3)
How would one know which exact precision and which effort setting to 
use, to recover at least 2 if not 3 points for the Mordell Weil basis??? 
Right now it appears that this is just hit-or-miss. So how do we aim to 
get the maximum hit? Some of the attempts come up empty-handed. This 
doesn't seem right.

Randall

e=[0,12304376939822994932659524,0,-3648259547053109398533591982691229700073064038400,0]
p=[[-999779060917633308399360,3866142351194747967608412122674782720],[-293883589543938115962240,1452405131779215974552917691531685120],[-1406975789099557808651520,5167717070222070579741742214157519360]]
print("e is a rank 4 curve with SHA > 1");
print("setting precision = 19");
default(realprecision,19);
E=ellinit(e);
print("ellrank(E)");
ellrank(E)
print("ellrank(E,2)");
ellrank(E,2)
print("ellrank(E,3)");
ellrank(E,3);
print("setting precision = 38");
default(realprecision,38);
E=ellinit(e);
print("ellrank(E)");
ellrank(E)
print("ellrank(E,2)");
ellrank(E,2)
print("ellrank(E,3)");
ellrank(E,3);
print("setting precision = 57");
default(realprecision,57);
E=ellinit(e);
print("ellrank(E)");
ellrank(E)
print("ellrank(E,2)");
ellrank(E,2)
print("ellrank(E,3)");
ellrank(E,3);
print("setting precision = 84");
default(realprecision,84);
E=ellinit(e);
print("ellrank(E)");
ellrank(E)
print("ellrank(E,2)");
ellrank(E,2)
print("ellrank(E,3)");
ellrank(E,3);
print("setting precision = 96");
default(realprecision,96);
E=ellinit(e);
print("ellrank(E)");
ellrank(E)
print("ellrank(E,2)");
ellrank(E,2)
print("ellrank(E,3)");
ellrank(E,3);
print("setting precision = 115");
default(realprecision,115);
E=ellinit(e);
print("ellrank(E)");
ellrank(E)
print("ellrank(E,2)");
ellrank(E,2)
print("ellrank(E,3)");
ellrank(E,3);