10.1.4.1 EllipticCurve_finite_field Objects

class EllipticCurve_finite_field
Elliptic curve over a finite field.
EllipticCurve_finite_field( x, [y=None])

Instances of class EllipticCurve_finite_field have the following methods (in addition to inherited methods and special methods):

abelian_group,$  $ cardinality,$  $ points

Further documentation:

abelian_group( )

Returns the abelian group structure of the group of points on this elliptic curve.

OUTPUT: - an abelian group - tuple of images of each of the generators of the abelian group as points on this curve

cardinality( [early_abort=False])

Return the number of points on this elliptic curve over this finite field.

INPUT:
    early_abort -- bool (default: Falst); if True an early abort technique
               is used and the computation is interrupted as soon
               as a small divisor of the order is detected.

Uses SEA (via sea.gp), as implemented in PARI by Christophe Doche and Sylvain Duquesne.

points( )

All the points on this elliptic curve.

Instances of class EllipticCurve_finite_field also have the following special methods:

__getitem__,$  $ _type

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