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We use Andrew Baker's analysis of the cofiber of the endomorphism of the$p$-adic elliptic spectrum ($p>3$) defined by multiplication by the `Hasseinvariant' $E_{p-1}$ to present its completion away from the locus of ordinaryelliptic curves as a sum of roughly $p/12$ copies (indexed by supesingularelliptic curves) of $p$-adic lifts of the height two mod $p$ cohomology theory$K(2)$. See a recent paper of Zhu Yifei for a much deeper exploration of thetopics considered in this note.

What $Ell$ sees that $K$ doesn't (when $p >3$)