… Using the theory of elliptic curves, we show that the class … of order 4 on a supersingular elliptic
curve (which is defined … of a supersingular curve lies in Fp2 , El is isomorphic to a curve E: …

… In §2 and §3 we study an elliptic curve E over Qp. In §2 … elliptic curve E over F, and give
some results which are consequences of a control theorem for Sel0(E/F). (If p is a supersingular …

… on supersingular j-invariants to supersingular elliptic curves with … , in terms of supersingular
elliptic curves with level, the … connection between supersingular elliptic curves and umbral …

… (ii) The Jacobian variety J(C) is isomorphic to a product of two supersingular elliptic
curves if and only if M = 0. (iii) The Jacobian variety J(C) is ordinary if and only if M has rank …

… F of characteristic p > 0 is called supersingular if its jacobian is isogenous to a product of
supersingular elliptic curves. An elliptic curve is called supersingular if it does not have points of …

… [12], where £ is a super singular elliptic curve. Let ψ be the polarization on A which is the …
of genus S 3 whose Jacobian is the product of supersingular elliptic curves we can ask …

… OUR CONTRIBUTIONS In this paper, we firstly optimize the hash function from supersingular
elliptic curve isogenies by taking advantage of the Weil restriction. This trick can transform …

… the knowledge of the endomorphism rings of the supersingular elliptic curves corresponding
to the vertices 0 and 1728. For a general supersingular elliptic curve E, it is very difficult to …

… problems for supersingular elliptic curves, their isogeny … endomorphism ring of a supersingular
elliptic curve, and computing … an isomorphism class of supersingular elliptic curves. The …

… Iwasawa theory for elliptic curves at supersingular primes. Throughout, we let E/Q be an
elliptic curve of conductor N, p > 3 be a prime of good supersingular reduction for E, and K/Q be …