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Jan 18 at 18:36 comment added Matthew Bolan Well, it works in the sense that if $L=K$ you have found a rational point. If $[L:K]=3$ then the three points $P^\sigma$ are colinear (same $y$ coordinate) and so sum to $\mathcal O$.
Jan 18 at 18:27 history asked わくわく CC BY-SA 4.0