discriminant curve

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• Discriminant — In algebra, the discriminant of a polynomial is an expression which gives information about the nature of the polynomial s roots. For example, the discriminant of the quadratic polynomial is Here, if Δ > 0, the polynomial has two real roots,… …   Wikipedia

• Elliptic curve — In mathematics, an elliptic curve 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 mdash; that is, it has a multiplication defined algebraically with… …   Wikipedia

• Courbe elliptique — Une sélection de courbes cubiques réelles définies par l équation y2 = x3 + ax + b.. La région montrée est [ − 3,3]2. La courbe pour a = b = 0 n est pas elliptique. En mathématiques, une courbe elliptique est un …   Wikipédia en Français

• History of algebra — Elementary algebra is the branch of mathematics that deals with solving for the operands of arithmetic equations. Modern or abstract algebra has its origins as an abstraction of elementary algebra. Historians know that the earliest mathematical… …   Wikipedia

• Degenerate conic — Main article: Conic section In mathematics, a degenerate conic is a conic (degree 2 plane curve, the zeros of a degree 2 polynomial equation, a quadratic) that fails to be an irreducible curve. This can happen in two ways: either it is a… …   Wikipedia

• Conic section — Types of conic sections: 1. Parabola 2. Circle and ellipse 3. Hyperbola …   Wikipedia

• Epsilon conjecture — The epsilon conjecture is a statement in number theory concerning properties of Galois representations associated with modular forms. It was proposed by Jean Pierre Serre and proved by Ken Ribet. The proof of epsilon conjecture was a significant… …   Wikipedia

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• Weierstrass's elliptic functions — In mathematics, Weierstrass s elliptic functions are elliptic functions that take a particularly simple form; they are named for Karl Weierstrass. This class of functions are also referred to as p functions and generally written using the symbol… …   Wikipedia

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• Algebraic number field — In mathematics, an algebraic number field (or simply number field) F is a finite (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector… …   Wikipedia