In mathematics, Felix Klein's j-invariant or j function, regarded as a function of a complex variable τ, is a modular function of weight zero for special...

of the normalized j-invariant exapand as, 1728   j ( τ ) = 1 / q + 744 + 196884 q + 21493760 q 2 + ⋯ {\displaystyle 1728{\text{ }}j(\tau...

The j-invariant of an elliptic curve given by the Weierstrass equation y 2 = x 3 + a x + b {\displaystyle y^{2}=x^{3}+ax+b} is given by the formula: j (...

In mathematics, an invariant is a property of a mathematical object (or a class of mathematical objects) which remains unchanged after operations or transformations...

J-function may refer to: The Klein j-invariant or j function in mathematics Leverett J-function in petroleum engineering This disambiguation page lists...

Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view...

Reshetikhin–Turaev invariant Tau-invariant I-Invariant Klein J-invariant Quantum isotopy invariant Ermakov–Lewis invariant Hermitian invariant Goussarov–Habiro theory...

It comes from the phrase "singular values of the j-invariant" used for values of the j-invariant for which a complex elliptic curve has complex multiplication...

of the j-invariant. In what follows, j(z) denotes the j-invariant of the complex number z. Briefly, j ( 1 + − d 2 ) {\displaystyle \textstyle j\left({\frac...

sense of algebraic geometry. Reversing this is accomplished by the j-invariant j(E), which can be used to determine τ and hence a torus. The set of all...

j, the second imaginary unit of a quaternion j, an index variable in a matrix The j-invariant, a modular function J, Joule, the SI unit of energy J,...

affine line, the coarse moduli space of elliptic curves, given by the j-invariant of an elliptic curve. It is a classical observation that every elliptic...

class invariant (or type invariant) is an invariant used for constraining objects of a class. Methods of the class should preserve the invariant. The class...

the (cyclic) image of the J-homomorphism, and the kernel of the Adams e-invariant (Adams 1966), a homomorphism from the stable homotopy groups to Q / Z...

coordinate: that is, both the Laplace–Beltrami operator and the curvature are invariant under isometries. Thus, for example, let S be a Riemann surface with metric...

smooth curve appears is described by the j-invariant in the table. Over the complex numbers, the curve with j-invariant 0 is the unique elliptic curve with...

equation Φn(x, y) = 0, such that (x, y) = (j(nτ), j(τ)) is a point on the curve. Here j(τ) denotes the j-invariant. The curve is sometimes called X0(n), though...

closely related concept is self-similarity, where a function or curve is invariant under a discrete subset of the dilations. It is also possible for the...

In computer science, a loop invariant is a property of a program loop that is true before (and after) each iteration. It is a logical assertion, sometimes...

reversible. These invariants therefore are only approximately invariant when describing a shape in a discrete image. The central moments μi j of any order...

approximately constant when changes occur slowly is called an adiabatic invariant. By this it is meant that if a system is varied between two end points...

decomposed forms 1⁄2 or ⁠1/2⁠ may be more appropriate. Division by two Sloane, N. J. A. (ed.). "Sequence A159907 (Numbers n with half-integral abundancy index...

lambda function Closely related are the modular forms, which include J-invariant Dedekind eta function Airy function Bessel functions: Defined by a differential...

745. 744 is a semiperfect number. It is also an abundant number. The j-invariant, an important function in the study of modular forms and Monstrous moonshine...

In control theory, a time-invariant (TI) system has a time-dependent system function that is not a direct function of time. Such systems are regarded...

tiling of the Poincaré disk is given in a natural way by the J-invariant, which is invariant under the modular group, and attains every complex number once...

In geometry, the Dehn invariant is a value used to determine whether one polyhedron can be cut into pieces and reassembled ("dissected") into another...

For example, the Chudnovsky algorithm involves in an essential way the j-invariant of an elliptic curve. Modular forms are holomorphic functions in the...

\mathbf {Q} } . This means that a formula expressing an invariant in terms of components, A i j {\displaystyle A_{ij}} , will give the same result for...

is invariant under the full modular group SL 2 ⁡ ( Z ) {\displaystyle \operatorname {SL} _{2}(\mathbb {Z} )} , and it is in fact Klein's modular j-invariant...