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Supersingular Elliptic Curve

A supersingular elliptic curve is an elliptic curve over a field of positive characteristic p whose group of geometric p-torsion points is trivial. Equivalently, its endomorphism ring over an algebraic closure, tensored with the rational numbers, is a quaternion algebra rather than an imaginary quadratic field. Supersingularity is preserved under extension of the base field and under isogeny.

For an elliptic curve over the finite field F_q, supersingularity can also be characterized by strong divisibility restrictions on the trace of its Frobenius endomorphism.

See also

Elliptic Curve, Finite Field, Isogeny, Torsion Point

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References

Silverman, J. H. The Arithmetic of Elliptic Curves, 2nd ed. New York: Springer-Verlag, 2009.

Cite this as:

Weisstein, Eric W. "Supersingular Elliptic Curve." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SupersingularEllipticCurve.html

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