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The cyclic twist of elliptic curve is a principally polarized abelian variety

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WHERE 234
WHERE 234
  • 85
  • 4

The cyclic twist of elliptic curve is principally polarized abelian variety

Let $L/K$ is a cyclic extension of degree $p$, and let $E/K$ be an elliptic curve.

Let $E^L$ be the kernel of the map $Res^L_{K}(E) \rightarrow E$, where $Res^L_{K}(E)$ is the Weil-restriction.

Is the twist $E^L$ principally polarized?