Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Elliptic_curve> ?p ?o. }
Showing items 1 to 62 of
62
with 100 items per page.
- Elliptic_curve abstract "In mathematics, an elliptic curve (EC) is a smooth, projective algebraic curve of genus one, on which there is a specified point O. An elliptic curve is in fact an abelian variety – that is, it has a multiplication defined algebraically, with respect to which it is a (necessarily commutative) group – and O serves as the identity element. Often the curve itself, without O specified, is called an elliptic curve.Any elliptic curve can be written as a plane algebraic curve defined by an equation of the form:which is non-singular; that is, its graph has no cusps or self-intersections. (When the characteristic of the coefficient field is equal to 2 or 3, the above equation is not quite general enough to comprise all non-singular cubic curves; see below for a more precise definition.) The point O is actually the "point at infinity" in the projective plane.If y2 = P(x), where P is any polynomial of degree three in x with no repeated roots, then we obtain a nonsingular plane curve of genus one, which is thus an elliptic curve. If P has degree four and is squarefree this equation again describes a plane curve of genus one; however, it has no natural choice of identity element. More generally, any algebraic curve of genus one, for example from the intersection of two quadric surfaces embedded in three-dimensional projective space, is called an elliptic curve, provided that it has at least one rational point to act as the identity.Using the theory of elliptic functions, it can be shown that elliptic curves defined over the complex numbers correspond to embeddings of the torus into the complex projective plane. The torus is also an abelian group, and in fact this correspondence is also a group isomorphism.Elliptic curves are especially important in number theory, and constitute a major area of current research; for example, they were used in the proof, by Andrew Wiles (assisted by Richard Taylor), of Fermat's Last Theorem. They also find applications in elliptic curve cryptography (ECC) and integer factorization.An elliptic curve is not an ellipse: see elliptic integral for the origin of the term. Topologically, a complex elliptic curve is a torus.".
- Elliptic_curve thumbnail EllipticCurveCatalog.svg?width=300.
- Elliptic_curve wikiPageExternalLink EFp_interactivo.
- Elliptic_curve wikiPageExternalLink ER_interactivo.
- Elliptic_curve wikiPageExternalLink 07468342.di020792.02p05747.pdf.
- Elliptic_curve wikiPageExternalLink thearithmeticofellipticcurves.
- Elliptic_curve wikiPageExternalLink 1126.
- Elliptic_curve wikiPageExternalLink ecc.
- Elliptic_curve wikiPageExternalLink ecc_javaCurve.html.
- Elliptic_curve wikiPageExternalLink Q.
- Elliptic_curve wikiPageExternalLink 14H52.html.
- Elliptic_curve wikiPageExternalLink loadFile.do?objectId=300&objectType=File.
- Elliptic_curve wikiPageExternalLink index.html.
- Elliptic_curve wikiPageID "10225".
- Elliptic_curve wikiPageRevisionID "606674358".
- Elliptic_curve hasPhotoCollection Elliptic_curve.
- Elliptic_curve id "3206".
- Elliptic_curve id "p/e035450".
- Elliptic_curve title "Elliptic Curves".
- Elliptic_curve title "Elliptic curve".
- Elliptic_curve title "Isogeny".
- Elliptic_curve urlname "EllipticCurve".
- Elliptic_curve subject Category:Analytic_number_theory.
- Elliptic_curve subject Category:Elliptic_curves.
- Elliptic_curve subject Category:Group_theory.
- Elliptic_curve type Abstraction100002137.
- Elliptic_curve type Attribute100024264.
- Elliptic_curve type Curve113867641.
- Elliptic_curve type EllipticCurves.
- Elliptic_curve type Line113863771.
- Elliptic_curve type Shape100027807.
- Elliptic_curve comment "In mathematics, an elliptic curve (EC) is a smooth, projective algebraic curve of genus one, on which there is a specified point O. An elliptic curve is in fact an abelian variety – that is, it has a multiplication defined algebraically, with respect to which it is a (necessarily commutative) group – and O serves as the identity element.".
- Elliptic_curve label "Courbe elliptique".
- Elliptic_curve label "Curva ellittica".
- Elliptic_curve label "Curva elíptica".
- Elliptic_curve label "Curva elíptica".
- Elliptic_curve label "Elliptic curve".
- Elliptic_curve label "Elliptische Kurve".
- Elliptic_curve label "Elliptische kromme".
- Elliptic_curve label "Krzywa eliptyczna".
- Elliptic_curve label "Эллиптическая кривая".
- Elliptic_curve label "منحنى إهليلجي".
- Elliptic_curve label "椭圆曲线".
- Elliptic_curve label "楕円曲線".
- Elliptic_curve sameAs Eliptická_křivka.
- Elliptic_curve sameAs Elliptische_Kurve.
- Elliptic_curve sameAs Ελλειπτική_καμπύλη.
- Elliptic_curve sameAs Curva_elíptica.
- Elliptic_curve sameAs Courbe_elliptique.
- Elliptic_curve sameAs Curva_ellittica.
- Elliptic_curve sameAs 楕円曲線.
- Elliptic_curve sameAs 타원곡선.
- Elliptic_curve sameAs Elliptische_kromme.
- Elliptic_curve sameAs Krzywa_eliptyczna.
- Elliptic_curve sameAs Curva_elíptica.
- Elliptic_curve sameAs m.02s3f.
- Elliptic_curve sameAs Q268493.
- Elliptic_curve sameAs Q268493.
- Elliptic_curve sameAs Elliptic_curve.
- Elliptic_curve wasDerivedFrom Elliptic_curve?oldid=606674358.
- Elliptic_curve depiction EllipticCurveCatalog.svg.
- Elliptic_curve isPrimaryTopicOf Elliptic_curve.