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Re:New Elliptic Curve Breaks 18-Year-Old Record by wbl on Wednesday November 13, 2024 @05:13PM (#42130706)
In this case there is a negation missing. If a line intersects three points we have A+B+C=0. To get the group law you have to negate a point.
Re:New Elliptic Curve Breaks 18-Year-Old Record by intuitionist on Wednesday November 13, 2024 @10:37PM (#42132929)
Of course for this to make sense you have to have a notion of 0, which is traditionally taken to be the point at infinity (so negation is negating the y-coordinate). It’s been a while since my algebraic geometry classes but IIRC this is just a useful convention.