Definition
Let K be a field with algebraic closure and E an elliptic curve over K. Then the -valued points have the structure of an abelian group. For every n, we have a multiplication map . Its kernel is denoted by . Now assume that the characteristic of K is p > 0. Then one can show that either
for r = 1, 2, 3, ... In the first case, E is called supersingular. Otherwise it is called ordinary. Of course, the term 'supersingular' does not mean that E is singular, since all elliptic curves are smooth.
Read more about this topic: Supersingular Elliptic Curve
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