For CM elliptic curves with j-invariant 0 or 1728, the p-Selmer rank of a twist is determined by the root number and a χ-component of a relative p-class group.
Number Theory 42 (1992), no
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Relative $p$-class groups and $p$-Selmer groups
For CM elliptic curves with j-invariant 0 or 1728, the p-Selmer rank of a twist is determined by the root number and a χ-component of a relative p-class group.