An algebraic curve over a field polynomial in coefficients in singular points over rational point is a point
field
The following table lists the names of algebraic curves of a given degree.
order curve examples 2 quadratic
curve circle , ellipse ,
hyperbola , parabola 3 cubic
curve cissoid of Diocles ,
conchoid of de Sluze , folium
of Descartes , Maclaurin trisectrix , Maltese cross curve , Mordell
curve , Ochoa curve , right
strophoid , semicubical parabola , serpentine
curve , Tschirnhausen cubic , witch
of Agnesi 4 quartic
curve ampersand curve ,
bean curve , bicorn , bicuspid
curve , bifoliate , bifolium ,
bitangent -rich curve, bow ,
bullet nose , butterfly
curve , capricornoid , cardioid ,
Cartesian ovals , Cassini
ovals , conchoid of Nicomedes , cruciform ,
deltoid , devil's curve ,
Dürer's conchoid , eight
curve , fish curve , hippopede ,
Kampyle of Eudoxus , Kepler's
folium , Klein quartic , knot
curve , lemniscate , limaçon ,
links curve , pear-shaped
curve , piriform curve , swastika
curve , trefoil curve , trifolium 5 quintic
curve Burnside curve ,
butterfly catastrophe curve, stirrup
curve 6 sextic
curve astroid , atriphtaloid ,
Cayley's sextic , cornoid ,
cycloid of Ceva , dumbbell
curve , ellipse evolute , epicycloid ,
Freeth's nephroid , heart
curve (first), limaçon evolute , nephroid , quadrifolium ,
scarabaeus curve , Talbot's
curve 8 octic
curve pear curve 12 dodecic curve ranunculoid
See also Algebraic Geometry ,
Algebraic
Variety ,
Curve
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References Arbarello, E.; Cornalba, M.; Griffiths, P. A.; and Harris, J. Geometry
of Algebraic Curves, I. Coolidge,
J. L. A
Treatise on Algebraic Plane Curves. Griffiths,
P. A. Introduction
to Algebraic Curves. Referenced
on Wolfram|Alpha Algebraic Curve
Cite this as:
Weisstein, Eric W. "Algebraic Curve."
From MathWorld https://mathworld.wolfram.com/AlgebraicCurve.html
Subject classifications
is an equation 
, where 
is a polynomial in 
and 
with coefficients in 
. A nonsingular algebraic curve is an
algebraic curve over 
which has no singular points over 
. A point on an algebraic curve is simply a solution of the
equation of the curve. A 
-rational point is a point
on the curve, where 
and 
are in the field 
.
