How to show that the following points are independent on elliptic curve $y^2=x^3-82x$ using Sage or any other software.
There is some determinant of certain matrix which I need to compute constructed from Néron-Tate height pairing. If this determinant is non-zero, then the points are independent. How to write a code to find this determinant? Three points on above curve are:
$[(-8,12),(-1,9),(49/4,231/8)]$