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- Imaginary_hyperelliptic_curve abstract "A hyperelliptic curve is a particular kind of algebraic curve. There exist hyperelliptic curves of every genus . If the genus of a hyperelliptic curve equals 1, we simply call the curve an elliptic curve. Hence we can see hyperelliptic curves as generalizations of elliptic curves. There is a well-known group structure on the set of points lying on an elliptic curve over some field , which we can describe geometrically with chords and tangents. Generalizing this group structure to the hyperelliptic case is not straightforward. We cannot define the same group law on the set of points lying on a hyperelliptic curve, instead a group structure can be defined on the so-called Jacobian of a hyperelliptic curve. The computations differ depending on the number of points at infinity. This article is about imaginary hyperelliptic curves, these are hyperelliptic curves with exactly 1 point at infinity. Real hyperelliptic curves have two points at infinity.".
- Imaginary_hyperelliptic_curve wikiPageID "21183334".
- Imaginary_hyperelliptic_curve wikiPageRevisionID "584151500".
- Imaginary_hyperelliptic_curve hasPhotoCollection Imaginary_hyperelliptic_curve.
- Imaginary_hyperelliptic_curve subject Category:Algebraic_curves.
- Imaginary_hyperelliptic_curve type Abstraction100002137.
- Imaginary_hyperelliptic_curve type AlgebraicCurves.
- Imaginary_hyperelliptic_curve type Attribute100024264.
- Imaginary_hyperelliptic_curve type Curve113867641.
- Imaginary_hyperelliptic_curve type Line113863771.
- Imaginary_hyperelliptic_curve type Shape100027807.
- Imaginary_hyperelliptic_curve comment "A hyperelliptic curve is a particular kind of algebraic curve. There exist hyperelliptic curves of every genus . If the genus of a hyperelliptic curve equals 1, we simply call the curve an elliptic curve. Hence we can see hyperelliptic curves as generalizations of elliptic curves. There is a well-known group structure on the set of points lying on an elliptic curve over some field , which we can describe geometrically with chords and tangents.".
- Imaginary_hyperelliptic_curve label "Imaginary hyperelliptic curve".
- Imaginary_hyperelliptic_curve sameAs m.05b_f09.
- Imaginary_hyperelliptic_curve sameAs Q6002519.
- Imaginary_hyperelliptic_curve sameAs Q6002519.
- Imaginary_hyperelliptic_curve sameAs Imaginary_hyperelliptic_curve.
- Imaginary_hyperelliptic_curve wasDerivedFrom Imaginary_hyperelliptic_curve?oldid=584151500.
- Imaginary_hyperelliptic_curve isPrimaryTopicOf Imaginary_hyperelliptic_curve.