question on the use of Weber's Functions

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

Hello:

I obtained from Andre Robatino back in the mid-1990's an elegant GP-Pari 
script which I modified to find the mock Heegner points for rank 1 
Congruent Number elliptic curves. I used his script to find the MW 
groups for all but 3 rank=2 curves for the first 1,000,000 elliptic curves.

The ingenious part of the script which Andre created uses Weber's 
functions and has an almost quadratic convergence to the non-torsion 
rational point on the curve. For example, I believe it took only 6 
passes for me to find the Mordell Weil generator for a point of height 
40593.31146980... which is very high on the rank=1 curve of n = 958957.

Has anyone here used Weber's functions to help find the rational points 
for the Mordell_Weil generators on the general rank=1 curve E(Q) ?

See https://dl.acm.org/doi/book/10.5555/922720

Andre gave me a copy of his master's thesis.

I am very intrigued that these Weber functions can possibly make a break 
through in finding the MW group (at least on rank=1 curves) in a much 
faster way than using Heegner points for general rank=1 curves.

Randall