supersingular

An elliptic curve $E$ over a field of characteristic $p$ defined by the cubic equation $f(w,x,y)=0$ is called supersingular if the coefficient of $(wxy)^{p-1}$ in $f(w,x,y)^{p-1}$ is zero.

A supersingular elliptic curve is said to have Hasse invariant $0$ ; an ordinary (i.e. non-supersingular) elliptic curve is said to have Hasse invariant $1$ .

This is equivalent to many other conditions. $E$ is supersingular iff the invariant differential is exact.Also, $E$ is supersingular iff $F^{*}:H^{1}(E,\\mathcal{O}_{E})\\to H^{1}(E,\\mathcal{O}_{E})$ is nonzero where $F^{*}$ is induced from the Frobenius morphism $F:E\\to E$ .

单词	Supersingular
释义	supersingular An elliptic curve $E$ over a field of characteristic $p$ defined by the cubic equation $f(w,x,y)=0$ is called supersingular if the coefficient of $(wxy)^{p-1}$ in $f(w,x,y)^{p-1}$ is zero. A supersingular elliptic curve is said to have Hasse invariant $0$ ; an ordinary (i.e. non-supersingular) elliptic curve is said to have Hasse invariant $1$ . This is equivalent to many other conditions. $E$ is supersingular iff the invariant differential is exact.Also, $E$ is supersingular iff $F^{}:H^{1}(E,\\mathcal{O}_{E})\\to H^{1}(E,\\mathcal{O}_{E})$ is nonzero where $F^{}$ is induced from the Frobenius morphism $F:E\\to E$ .
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