Proof: BoolElt Default: true
Given an elliptic curve E over a finite field, this function returns
false if E is ordinary, otherwise proves that E is supersingular
and returns true.
If the parameter Proof is set to false then the effect of
the function is the same as that of IsProbablySupersingular.
Given a prime p, returns the separable monic polynomial over Fp whose
roots are precisely the j invariants of supersingular elliptic curves in
characteristic p.
The polynomial is computed by a formula; ignoring factors corresponding to
j=0 or 1728, it is the partial power-series expansion of a certain
hypergeometric function reduced mod p.
For p of moderate size this is a very fast method.
Given an elliptic curve E over a finite field, this function returns
true if the elliptic curve E is ordinary, otherwise false
(i.e., if it is supersingular). Thus, this function is the logical negation
of IsSupersingular.
Given an elliptic curve E over a finite field, this function returns
returns false if the elliptic curve E is proved to be ordinary,
otherwise true. The algorithm is nondeterministic and repeated
tests are independent.
V2.28, 13 July 2023