Let $E/\mathbb{Q}$ is an elliptic curve. So clearly $E$ is a principal homogeneous space for $E$. Now I'm getting trouble to understand this statement saying, any other principal homogeneous space is in the same class of $E$ iff it has a point in $\mathbb{Q}$. Could anyone please explain this ?
2026-04-01 00:28:37.1775003317
a principal homogeneous space is in the trivial class iff it has a point in $\mathbb{Q} ?$
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