Re: another simple question

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

To all:

I am not sure how my post got misinterpreted, maybe this is my fault??? 
I would be interested in your comments.

When I said that many elliptic curves can be found with the point [1/2, 
5/8], I meant curves with the Weierstrass format [a1,a2,a3,a4,a6] with 
all coefficients a1..a6 in Q, not Z.

Below are 458 curves which contain [1/2, 5/8] using the reduced 
fractions for 1/2 to 99/100 and the 32 possible combinations of +/- for 
the 5 coefficients.

I hope this helps everyone to understand my question.  Did I make a 
mistake in my post? While we could use lindep to quickly find the 
correct elliptic curve, my mind is struggling with the situation given 
below.

Randall

owner@localhost:~/math/Diophantine/m-tuples> cat 001
[1/2, -1/2, -1/2, 1/2, -1/64]
[-1/2, 1/2, 1/2, 1/2, 3/64]
[-1/2, 1/2, -1/2, -1/2, -5/64]
[-1/2, -1/2, -1/2, -1/2, 11/64]
[1/2, 1/2, -1/2, -1/2, 15/64]
[1/2, 1/2, -1/2, 1/2, -17/64]
[-1/2, -1/2, 1/2, 1/2, 19/64]
[-1/2, -1/2, -1/2, 1/2, -21/64]
[1/2, 1/2, 1/2, 1/2, 23/64]
[1/2, -1/2, -1/2, -1/2, 31/64]
[-1/2, 1/2, 1/2, -1/2, 35/64]
[-1/2, 1/2, -1/2, 1/2, -37/64]
[1/2, -1/2, 1/2, 1/2, 39/64]
[-1/2, -1/2, 1/2, -1/2, 51/64]
[1/2, 1/2, 1/2, -1/2, 55/64]
[-1/2, -1/2, -1/2, -1/4, 3/64]
[1/2, 1/2, -1/2, -1/4, 7/64]
[1/2, -1/2, -1/2, 1/4, 7/64]
[1/2, 1/2, -1/2, 1/4, -9/64]
[-1/2, 1/2, 1/2, 1/4, 11/64]
[-1/2, 1/2, -1/2, -1/4, -13/64]
[-1/2, -1/2, -1/2, 1/4, -13/64]
[1/2, -1/2, -1/2, -1/4, 23/64]
[-1/2, 1/2, 1/2, -1/4, 27/64]
[-1/2, -1/2, 1/2, 1/4, 27/64]
[-1/2, 1/2, -1/2, 1/4, -29/64]
[1/2, 1/2, 1/2, 1/4, 31/64]
[-1/2, -1/2, 1/2, -1/4, 43/64]
[1/2, 1/2, 1/2, -1/4, 47/64]
[1/2, -1/2, 1/2, 1/4, 47/64]
[1/2, -1/2, 1/2, -1/4, 63/64]
[-1/2, 1/2, -1/2, -3/4, 3/64]
[-1/2, 1/2, 1/2, 3/4, -5/64]
[1/2, -1/2, -1/2, 3/4, -9/64]
[-1/2, -1/2, 1/2, 3/4, 11/64]
[1/2, 1/2, 1/2, 3/4, 15/64]
[-1/2, -1/2, -1/2, -3/4, 19/64]
[1/2, 1/2, -1/2, -3/4, 23/64]
[1/2, 1/2, -1/2, 3/4, -25/64]
[-1/2, -1/2, -1/2, 3/4, -29/64]
[1/2, -1/2, 1/2, 3/4, 31/64]
[1/2, -1/2, -1/2, -3/4, 39/64]
[-1/2, 1/2, 1/2, -3/4, 43/64]
[-1/2, 1/2, -1/2, 3/4, -45/64]
[-1/2, -1/2, 1/2, -3/4, 59/64]
[1/2, 1/2, 1/2, -3/4, 63/64]
[-1/2, -1/2, -1/2, -1/8, -1/64]
[1/2, 1/2, -1/2, -1/8, 3/64]
[1/2, 1/2, -1/2, 1/8, -5/64]
[-1/2, -1/2, -1/2, 1/8, -9/64]
[1/2, -1/2, -1/2, 1/8, 11/64]
[-1/2, 1/2, 1/2, 1/8, 15/64]
[-1/2, 1/2, -1/2, -1/8, -17/64]
[1/2, -1/2, -1/2, -1/8, 19/64]
[-1/2, 1/2, 1/2, -1/8, 23/64]
[-1/2, 1/2, -1/2, 1/8, -25/64]
[-1/2, -1/2, 1/2, 1/8, 31/64]
[1/2, 1/2, 1/2, 1/8, 35/64]
[-1/2, -1/2, 1/2, -1/8, 39/64]
[1/2, 1/2, 1/2, -1/8, 43/64]
[1/2, -1/2, 1/2, 1/8, 51/64]
[1/2, -1/2, 1/2, -1/8, 59/64]
[1/2, -1/2, -1/2, 3/8, 3/64]
[-1/2, 1/2, 1/2, 3/8, 7/64]
[-1/2, -1/2, -1/2, -3/8, 7/64]
[-1/2, 1/2, -1/2, -3/8, -9/64]
[1/2, 1/2, -1/2, -3/8, 11/64]
[1/2, 1/2, -1/2, 3/8, -13/64]
[-1/2, -1/2, -1/2, 3/8, -17/64]
[-1/2, -1/2, 1/2, 3/8, 23/64]
[1/2, 1/2, 1/2, 3/8, 27/64]
[1/2, -1/2, -1/2, -3/8, 27/64]
[-1/2, 1/2, 1/2, -3/8, 31/64]
[-1/2, 1/2, -1/2, 3/8, -33/64]
[1/2, -1/2, 1/2, 3/8, 43/64]
[-1/2, -1/2, 1/2, -3/8, 47/64]
[1/2, 1/2, 1/2, -3/8, 51/64]
[-1/2, 1/2, 1/2, 5/8, -1/64]
[-1/2, 1/2, -1/2, -5/8, -1/64]
[1/2, -1/2, -1/2, 5/8, -5/64]
[-1/2, -1/2, 1/2, 5/8, 15/64]
[-1/2, -1/2, -1/2, -5/8, 15/64]
[1/2, 1/2, 1/2, 5/8, 19/64]
[1/2, 1/2, -1/2, -5/8, 19/64]
[1/2, 1/2, -1/2, 5/8, -21/64]
[-1/2, -1/2, -1/2, 5/8, -25/64]
[1/2, -1/2, 1/2, 5/8, 35/64]
[1/2, -1/2, -1/2, -5/8, 35/64]
[-1/2, 1/2, 1/2, -5/8, 39/64]
[-1/2, 1/2, -1/2, 5/8, -41/64]
[-1/2, -1/2, 1/2, -5/8, 55/64]
[1/2, 1/2, 1/2, -5/8, 59/64]
[-1/2, 1/2, -1/2, -7/8, 7/64]
[-1/2, -1/2, 1/2, 7/8, 7/64]
[-1/2, 1/2, 1/2, 7/8, -9/64]
[1/2, 1/2, 1/2, 7/8, 11/64]
[1/2, -1/2, -1/2, 7/8, -13/64]
[-1/2, -1/2, -1/2, -7/8, 23/64]
[1/2, 1/2, -1/2, -7/8, 27/64]
[1/2, -1/2, 1/2, 7/8, 27/64]
[1/2, 1/2, -1/2, 7/8, -29/64]
[-1/2, -1/2, -1/2, 7/8, -33/64]
[1/2, -1/2, -1/2, -7/8, 43/64]
[-1/2, 1/2, 1/2, -7/8, 47/64]
[-1/2, 1/2, -1/2, 7/8, -49/64]
[-1/2, -1/2, 1/2, -7/8, 63/64]
[1/2, 1/2, -1/2, -1/16, 1/64]
[1/2, 1/2, -1/2, 1/16, -3/64]
[-1/2, -1/2, -1/2, -1/16, -3/64]
[-1/2, -1/2, -1/2, 1/16, -7/64]
[1/2, -1/2, -1/2, 1/16, 13/64]
[1/2, -1/2, -1/2, -1/16, 17/64]
[-1/2, 1/2, 1/2, 1/16, 17/64]
[-1/2, 1/2, -1/2, -1/16, -19/64]
[-1/2, 1/2, 1/2, -1/16, 21/64]
[-1/2, 1/2, -1/2, 1/16, -23/64]
[-1/2, -1/2, 1/2, 1/16, 33/64]
[1/2, 1/2, 1/2, 1/16, 37/64]
[-1/2, -1/2, 1/2, -1/16, 37/64]
[1/2, 1/2, 1/2, -1/16, 41/64]
[1/2, -1/2, 1/2, 1/16, 53/64]
[1/2, -1/2, 1/2, -1/16, 57/64]
[-1/2, -1/2, -1/2, -3/16, 1/64]
[1/2, 1/2, -1/2, -3/16, 5/64]
[1/2, 1/2, -1/2, 3/16, -7/64]
[1/2, -1/2, -1/2, 3/16, 9/64]
[-1/2, -1/2, -1/2, 3/16, -11/64]
[-1/2, 1/2, 1/2, 3/16, 13/64]
[-1/2, 1/2, -1/2, -3/16, -15/64]
[1/2, -1/2, -1/2, -3/16, 21/64]
[-1/2, 1/2, 1/2, -3/16, 25/64]
[-1/2, 1/2, -1/2, 3/16, -27/64]
[-1/2, -1/2, 1/2, 3/16, 29/64]
[1/2, 1/2, 1/2, 3/16, 33/64]
[-1/2, -1/2, 1/2, -3/16, 41/64]
[1/2, 1/2, 1/2, -3/16, 45/64]
[1/2, -1/2, 1/2, 3/16, 49/64]
[1/2, -1/2, 1/2, -3/16, 61/64]
[1/2, -1/2, -1/2, 5/16, 5/64]
[-1/2, -1/2, -1/2, -5/16, 5/64]
[1/2, 1/2, -1/2, -5/16, 9/64]
[-1/2, 1/2, 1/2, 5/16, 9/64]
[1/2, 1/2, -1/2, 5/16, -11/64]
[-1/2, 1/2, -1/2, -5/16, -11/64]
[-1/2, -1/2, -1/2, 5/16, -15/64]
[1/2, -1/2, -1/2, -5/16, 25/64]
[-1/2, -1/2, 1/2, 5/16, 25/64]
[1/2, 1/2, 1/2, 5/16, 29/64]
[-1/2, 1/2, 1/2, -5/16, 29/64]
[-1/2, 1/2, -1/2, 5/16, -31/64]
[1/2, -1/2, 1/2, 5/16, 45/64]
[-1/2, -1/2, 1/2, -5/16, 45/64]
[1/2, 1/2, 1/2, -5/16, 49/64]
[1/2, -1/2, -1/2, 7/16, 1/64]
[-1/2, 1/2, 1/2, 7/16, 5/64]
[-1/2, 1/2, -1/2, -7/16, -7/64]
[-1/2, -1/2, -1/2, -7/16, 9/64]
[1/2, 1/2, -1/2, -7/16, 13/64]
[1/2, 1/2, -1/2, 7/16, -15/64]
[-1/2, -1/2, -1/2, 7/16, -19/64]
[-1/2, -1/2, 1/2, 7/16, 21/64]
[1/2, 1/2, 1/2, 7/16, 25/64]
[1/2, -1/2, -1/2, -7/16, 29/64]
[-1/2, 1/2, 1/2, -7/16, 33/64]
[-1/2, 1/2, -1/2, 7/16, -35/64]
[1/2, -1/2, 1/2, 7/16, 41/64]
[-1/2, -1/2, 1/2, -7/16, 49/64]
[1/2, 1/2, 1/2, -7/16, 53/64]
[-1/2, 1/2, 1/2, 9/16, 1/64]
[1/2, -1/2, -1/2, 9/16, -3/64]
[-1/2, 1/2, -1/2, -9/16, -3/64]
[-1/2, -1/2, -1/2, -9/16, 13/64]
[1/2, 1/2, -1/2, -9/16, 17/64]
[-1/2, -1/2, 1/2, 9/16, 17/64]
[1/2, 1/2, -1/2, 9/16, -19/64]
[1/2, 1/2, 1/2, 9/16, 21/64]
[-1/2, -1/2, -1/2, 9/16, -23/64]
[1/2, -1/2, -1/2, -9/16, 33/64]
[1/2, -1/2, 1/2, 9/16, 37/64]
[-1/2, 1/2, 1/2, -9/16, 37/64]
[-1/2, 1/2, -1/2, 9/16, -39/64]
[-1/2, -1/2, 1/2, -9/16, 53/64]
[1/2, 1/2, 1/2, -9/16, 57/64]
[-1/2, 1/2, -1/2, -11/16, 1/64]
[-1/2, 1/2, 1/2, 11/16, -3/64]
[1/2, -1/2, -1/2, 11/16, -7/64]
[-1/2, -1/2, 1/2, 11/16, 13/64]
[1/2, 1/2, 1/2, 11/16, 17/64]
[-1/2, -1/2, -1/2, -11/16, 17/64]
[1/2, 1/2, -1/2, -11/16, 21/64]
[1/2, 1/2, -1/2, 11/16, -23/64]
[-1/2, -1/2, -1/2, 11/16, -27/64]
[1/2, -1/2, 1/2, 11/16, 33/64]
[1/2, -1/2, -1/2, -11/16, 37/64]
[-1/2, 1/2, 1/2, -11/16, 41/64]
[-1/2, 1/2, -1/2, 11/16, -43/64]
[-1/2, -1/2, 1/2, -11/16, 57/64]
[1/2, 1/2, 1/2, -11/16, 61/64]
[-1/2, 1/2, -1/2, -13/16, 5/64]
[-1/2, 1/2, 1/2, 13/16, -7/64]
[-1/2, -1/2, 1/2, 13/16, 9/64]
[1/2, -1/2, -1/2, 13/16, -11/64]
[1/2, 1/2, 1/2, 13/16, 13/64]
[-1/2, -1/2, -1/2, -13/16, 21/64]
[1/2, 1/2, -1/2, -13/16, 25/64]
[1/2, 1/2, -1/2, 13/16, -27/64]
[1/2, -1/2, 1/2, 13/16, 29/64]
[-1/2, -1/2, -1/2, 13/16, -31/64]
[1/2, -1/2, -1/2, -13/16, 41/64]
[-1/2, 1/2, 1/2, -13/16, 45/64]
[-1/2, 1/2, -1/2, 13/16, -47/64]
[-1/2, -1/2, 1/2, -13/16, 61/64]
[-1/2, -1/2, 1/2, 15/16, 5/64]
[1/2, 1/2, 1/2, 15/16, 9/64]
[-1/2, 1/2, -1/2, -15/16, 9/64]
[-1/2, 1/2, 1/2, 15/16, -11/64]
[1/2, -1/2, -1/2, 15/16, -15/64]
[1/2, -1/2, 1/2, 15/16, 25/64]
[-1/2, -1/2, -1/2, -15/16, 25/64]
[1/2, 1/2, -1/2, -15/16, 29/64]
[1/2, 1/2, -1/2, 15/16, -31/64]
[-1/2, -1/2, -1/2, 15/16, -35/64]
[1/2, -1/2, -1/2, -15/16, 45/64]
[-1/2, 1/2, 1/2, -15/16, 49/64]
[-1/2, 1/2, -1/2, 15/16, -51/64]
[1/2, -1/2, -1/2, -1/32, 1/4]
[1/2, 1/2, 1/2, -1/32, 5/8]
[1/2, -1/2, 1/2, -1/32, 7/8]
[-1/2, -1/2, -1/2, -1/32, -1/16]
[-1/2, 1/2, 1/2, -1/32, 5/16]
[-1/2, 1/2, -1/2, -1/32, -5/16]
[-1/2, -1/2, 1/2, -1/32, 9/16]
[1/2, 1/2, -1/2, 1/32, -1/32]
[-1/2, -1/2, -1/2, 1/32, -3/32]
[1/2, -1/2, -1/2, 1/32, 7/32]
[-1/2, 1/2, 1/2, 1/32, 9/32]
[-1/2, 1/2, -1/2, 1/32, -11/32]
[-1/2, -1/2, 1/2, 1/32, 17/32]
[1/2, 1/2, 1/2, 1/32, 19/32]
[1/2, -1/2, 1/2, 1/32, 27/32]
[-1/2, -1/2, 1/2, 3/32, 1/2]
[-1/2, 1/2, 1/2, 3/32, 1/4]
[-1/2, -1/2, -1/2, 3/32, -1/8]
[-1/2, 1/2, -1/2, 3/32, -3/8]
[1/2, 1/2, -1/2, 3/32, -1/16]
[1/2, -1/2, -1/2, 3/32, 3/16]
[1/2, 1/2, 1/2, 3/32, 9/16]
[1/2, -1/2, 1/2, 3/32, 13/16]
[1/2, 1/2, -1/2, -3/32, 1/32]
[-1/2, -1/2, -1/2, -3/32, -1/32]
[1/2, -1/2, -1/2, -3/32, 9/32]
[-1/2, 1/2, -1/2, -3/32, -9/32]
[-1/2, 1/2, 1/2, -3/32, 11/32]
[-1/2, -1/2, 1/2, -3/32, 19/32]
[1/2, 1/2, 1/2, -3/32, 21/32]
[1/2, -1/2, 1/2, -3/32, 29/32]
[-1/2, 1/2, -1/2, -5/32, -1/4]
[-1/2, 1/2, 1/2, -5/32, 3/8]
[-1/2, -1/2, 1/2, -5/32, 5/8]
[1/2, 1/2, -1/2, -5/32, 1/16]
[1/2, -1/2, -1/2, -5/32, 5/16]
[1/2, 1/2, 1/2, -5/32, 11/16]
[1/2, -1/2, 1/2, -5/32, 15/16]
[1/2, 1/2, -1/2, 5/32, -3/32]
[1/2, -1/2, -1/2, 5/32, 5/32]
[-1/2, -1/2, -1/2, 5/32, -5/32]
[-1/2, 1/2, 1/2, 5/32, 7/32]
[-1/2, 1/2, -1/2, 5/32, -13/32]
[-1/2, -1/2, 1/2, 5/32, 15/32]
[1/2, 1/2, 1/2, 5/32, 17/32]
[1/2, -1/2, 1/2, 5/32, 25/32]
[1/2, 1/2, 1/2, 7/32, 1/2]
[1/2, -1/2, 1/2, 7/32, 3/4]
[1/2, 1/2, -1/2, 7/32, -1/8]
[1/2, -1/2, -1/2, 7/32, 1/8]
[-1/2, 1/2, 1/2, 7/32, 3/16]
[-1/2, -1/2, -1/2, 7/32, -3/16]
[-1/2, 1/2, -1/2, 7/32, -7/16]
[-1/2, -1/2, 1/2, 7/32, 7/16]
[-1/2, -1/2, -1/2, -7/32, 1/32]
[1/2, 1/2, -1/2, -7/32, 3/32]
[-1/2, 1/2, -1/2, -7/32, -7/32]
[1/2, -1/2, -1/2, -7/32, 11/32]
[-1/2, 1/2, 1/2, -7/32, 13/32]
[-1/2, -1/2, 1/2, -7/32, 21/32]
[1/2, 1/2, 1/2, -7/32, 23/32]
[1/2, -1/2, 1/2, -7/32, 31/32]
[1/2, 1/2, 1/2, -9/32, 3/4]
[1/2, 1/2, -1/2, -9/32, 1/8]
[1/2, -1/2, -1/2, -9/32, 3/8]
[-1/2, -1/2, -1/2, -9/32, 1/16]
[-1/2, 1/2, -1/2, -9/32, -3/16]
[-1/2, 1/2, 1/2, -9/32, 7/16]
[-1/2, -1/2, 1/2, -9/32, 11/16]
[1/2, -1/2, -1/2, 9/32, 3/32]
[1/2, 1/2, -1/2, 9/32, -5/32]
[-1/2, 1/2, 1/2, 9/32, 5/32]
[-1/2, -1/2, -1/2, 9/32, -7/32]
[-1/2, -1/2, 1/2, 9/32, 13/32]
[1/2, 1/2, 1/2, 9/32, 15/32]
[-1/2, 1/2, -1/2, 9/32, -15/32]
[1/2, -1/2, 1/2, 9/32, 23/32]
[-1/2, 1/2, -1/2, 11/32, -1/2]
[-1/2, -1/2, -1/2, 11/32, -1/4]
[-1/2, 1/2, 1/2, 11/32, 1/8]
[-1/2, -1/2, 1/2, 11/32, 3/8]
[1/2, -1/2, -1/2, 11/32, 1/16]
[1/2, 1/2, -1/2, 11/32, -3/16]
[1/2, 1/2, 1/2, 11/32, 7/16]
[1/2, -1/2, 1/2, 11/32, 11/16]
[-1/2, -1/2, -1/2, -11/32, 3/32]
[1/2, 1/2, -1/2, -11/32, 5/32]
[-1/2, 1/2, -1/2, -11/32, -5/32]
[1/2, -1/2, -1/2, -11/32, 13/32]
[-1/2, 1/2, 1/2, -11/32, 15/32]
[-1/2, -1/2, 1/2, -11/32, 23/32]
[1/2, 1/2, 1/2, -11/32, 25/32]
[-1/2, 1/2, 1/2, -13/32, 1/2]
[-1/2, -1/2, 1/2, -13/32, 3/4]
[-1/2, 1/2, -1/2, -13/32, -1/8]
[-1/2, -1/2, -1/2, -13/32, 1/8]
[1/2, 1/2, -1/2, -13/32, 3/16]
[1/2, -1/2, -1/2, -13/32, 7/16]
[1/2, 1/2, 1/2, -13/32, 13/16]
[1/2, -1/2, -1/2, 13/32, 1/32]
[-1/2, 1/2, 1/2, 13/32, 3/32]
[1/2, 1/2, -1/2, 13/32, -7/32]
[-1/2, -1/2, -1/2, 13/32, -9/32]
[-1/2, -1/2, 1/2, 13/32, 11/32]
[1/2, 1/2, 1/2, 13/32, 13/32]
[-1/2, 1/2, -1/2, 13/32, -17/32]
[1/2, -1/2, 1/2, 13/32, 21/32]
[1/2, 1/2, -1/2, 15/32, -1/4]
[1/2, 1/2, 1/2, 15/32, 3/8]
[1/2, -1/2, 1/2, 15/32, 5/8]
[-1/2, 1/2, 1/2, 15/32, 1/16]
[-1/2, -1/2, 1/2, 15/32, 5/16]
[-1/2, -1/2, -1/2, 15/32, -5/16]
[-1/2, 1/2, -1/2, 15/32, -9/16]
[-1/2, 1/2, -1/2, -15/32, -3/32]
[-1/2, -1/2, -1/2, -15/32, 5/32]
[1/2, 1/2, -1/2, -15/32, 7/32]
[1/2, -1/2, -1/2, -15/32, 15/32]
[-1/2, 1/2, 1/2, -15/32, 17/32]
[-1/2, -1/2, 1/2, -15/32, 25/32]
[1/2, 1/2, 1/2, -15/32, 27/32]
[1/2, -1/2, -1/2, -17/32, 1/2]
[1/2, 1/2, -1/2, -17/32, 1/4]
[1/2, 1/2, 1/2, -17/32, 7/8]
[-1/2, 1/2, -1/2, -17/32, -1/16]
[-1/2, -1/2, -1/2, -17/32, 3/16]
[-1/2, 1/2, 1/2, -17/32, 9/16]
[-1/2, -1/2, 1/2, -17/32, 13/16]
[1/2, -1/2, -1/2, 17/32, -1/32]
[-1/2, 1/2, 1/2, 17/32, 1/32]
[1/2, 1/2, -1/2, 17/32, -9/32]
[-1/2, -1/2, 1/2, 17/32, 9/32]
[1/2, 1/2, 1/2, 17/32, 11/32]
[-1/2, -1/2, -1/2, 17/32, -11/32]
[1/2, -1/2, 1/2, 17/32, 19/32]
[-1/2, 1/2, -1/2, 17/32, -19/32]
[-1/2, -1/2, 1/2, 19/32, 1/4]
[-1/2, -1/2, -1/2, 19/32, -3/8]
[-1/2, 1/2, -1/2, 19/32, -5/8]
[1/2, -1/2, -1/2, 19/32, -1/16]
[1/2, 1/2, 1/2, 19/32, 5/16]
[1/2, 1/2, -1/2, 19/32, -5/16]
[1/2, -1/2, 1/2, 19/32, 9/16]
[-1/2, 1/2, -1/2, -19/32, -1/32]
[-1/2, -1/2, -1/2, -19/32, 7/32]
[1/2, 1/2, -1/2, -19/32, 9/32]
[1/2, -1/2, -1/2, -19/32, 17/32]
[-1/2, 1/2, 1/2, -19/32, 19/32]
[-1/2, -1/2, 1/2, -19/32, 27/32]
[1/2, 1/2, 1/2, -19/32, 29/32]
[-1/2, -1/2, -1/2, -21/32, 1/4]
[-1/2, 1/2, 1/2, -21/32, 5/8]
[-1/2, -1/2, 1/2, -21/32, 7/8]
[1/2, 1/2, -1/2, -21/32, 5/16]
[1/2, -1/2, -1/2, -21/32, 9/16]
[1/2, 1/2, 1/2, -21/32, 15/16]
[-1/2, 1/2, 1/2, 21/32, -1/32]
[1/2, -1/2, -1/2, 21/32, -3/32]
[-1/2, -1/2, 1/2, 21/32, 7/32]
[1/2, 1/2, 1/2, 21/32, 9/32]
[1/2, 1/2, -1/2, 21/32, -11/32]
[-1/2, -1/2, -1/2, 21/32, -13/32]
[1/2, -1/2, 1/2, 21/32, 17/32]
[-1/2, 1/2, -1/2, 21/32, -21/32]
[1/2, -1/2, 1/2, 23/32, 1/2]
[1/2, 1/2, 1/2, 23/32, 1/4]
[1/2, -1/2, -1/2, 23/32, -1/8]
[1/2, 1/2, -1/2, 23/32, -3/8]
[-1/2, 1/2, 1/2, 23/32, -1/16]
[-1/2, -1/2, 1/2, 23/32, 3/16]
[-1/2, -1/2, -1/2, 23/32, -7/16]
[-1/2, 1/2, -1/2, 23/32, -11/16]
[-1/2, 1/2, -1/2, -23/32, 1/32]
[-1/2, -1/2, -1/2, -23/32, 9/32]
[1/2, 1/2, -1/2, -23/32, 11/32]
[1/2, -1/2, -1/2, -23/32, 19/32]
[-1/2, 1/2, 1/2, -23/32, 21/32]
[-1/2, -1/2, 1/2, -23/32, 29/32]
[1/2, 1/2, 1/2, -23/32, 31/32]
[1/2, 1/2, -1/2, -25/32, 3/8]
[1/2, -1/2, -1/2, -25/32, 5/8]
[-1/2, 1/2, -1/2, -25/32, 1/16]
[-1/2, -1/2, -1/2, -25/32, 5/16]
[-1/2, 1/2, 1/2, -25/32, 11/16]
[-1/2, -1/2, 1/2, -25/32, 15/16]
[-1/2, 1/2, 1/2, 25/32, -3/32]
[1/2, -1/2, -1/2, 25/32, -5/32]
[-1/2, -1/2, 1/2, 25/32, 5/32]
[1/2, 1/2, 1/2, 25/32, 7/32]
[1/2, 1/2, -1/2, 25/32, -13/32]
[1/2, -1/2, 1/2, 25/32, 15/32]
[-1/2, -1/2, -1/2, 25/32, -15/32]
[-1/2, 1/2, -1/2, 25/32, -23/32]
[-1/2, -1/2, -1/2, 27/32, -1/2]
[-1/2, 1/2, -1/2, 27/32, -3/4]
[-1/2, 1/2, 1/2, 27/32, -1/8]
[-1/2, -1/2, 1/2, 27/32, 1/8]
[1/2, 1/2, 1/2, 27/32, 3/16]
[1/2, -1/2, -1/2, 27/32, -3/16]
[1/2, 1/2, -1/2, 27/32, -7/16]
[1/2, -1/2, 1/2, 27/32, 7/16]
[-1/2, 1/2, -1/2, -27/32, 3/32]
[-1/2, -1/2, -1/2, -27/32, 11/32]
[1/2, 1/2, -1/2, -27/32, 13/32]
[1/2, -1/2, -1/2, -27/32, 21/32]
[-1/2, 1/2, 1/2, -27/32, 23/32]
[-1/2, -1/2, 1/2, -27/32, 31/32]
[-1/2, 1/2, 1/2, -29/32, 3/4]
[-1/2, 1/2, -1/2, -29/32, 1/8]
[-1/2, -1/2, -1/2, -29/32, 3/8]
[1/2, 1/2, -1/2, -29/32, 7/16]
[1/2, -1/2, -1/2, -29/32, 11/16]
[-1/2, -1/2, 1/2, 29/32, 3/32]
[1/2, 1/2, 1/2, 29/32, 5/32]
[-1/2, 1/2, 1/2, 29/32, -5/32]
[1/2, -1/2, -1/2, 29/32, -7/32]
[1/2, -1/2, 1/2, 29/32, 13/32]
[1/2, 1/2, -1/2, 29/32, -15/32]
[-1/2, -1/2, -1/2, 29/32, -17/32]
[-1/2, 1/2, -1/2, 29/32, -25/32]
[1/2, 1/2, -1/2, 31/32, -1/2]
[1/2, -1/2, -1/2, 31/32, -1/4]
[1/2, 1/2, 1/2, 31/32, 1/8]
[1/2, -1/2, 1/2, 31/32, 3/8]
[-1/2, -1/2, 1/2, 31/32, 1/16]
[-1/2, 1/2, 1/2, 31/32, -3/16]
[-1/2, -1/2, -1/2, 31/32, -9/16]
[-1/2, 1/2, -1/2, 31/32, -13/16]
[-1/2, 1/2, -1/2, -31/32, 5/32]
[-1/2, -1/2, -1/2, -31/32, 13/32]
[1/2, 1/2, -1/2, -31/32, 15/32]
[1/2, -1/2, -1/2, -31/32, 23/32]
[-1/2, 1/2, 1/2, -31/32, 25/32]

On 4/16/24 20:45, American Citizen wrote:
> Recently, we saw a point with thousands of digits posted with the 
> question, what elliptic curve might have this point?
>
> The answer was to use lindep to determine the elliptic curve, and so 
> everything went fine.
>
> However, I am dubious that this general approach using lindep on [y^2, 
> xy, y, x^3, x^2, x, 1] will work when we have points of lesser heights.
>
> Suppose we have the point [1/2, 5/8] ??
>
> I strongly suspect that thousands perhaps millions, maybe more? 
> elliptic curves can be found containing this point.
>
> How can we effectively pare down the possibilities to something we can 
> work with?
>
> Randall