American Citizen on Mon, 11 Dec 2023 04:55:15 +0100 |
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question on the use of Weber's Functions |
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