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...

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

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,...

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 (...

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...

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...

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...

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

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...

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...

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...

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...

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...

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...

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

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

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...

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...

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

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...

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...

degree term of the expansion of Klein's j-invariant, and the zeroth degree term of the Laurent series of the J-invariant. Furthermore, 744 = 3 × 248 where 248...

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...

\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...

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...

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...

known exceptional sets: Klein's j-invariant E ( j ) = { α ∈ H : [ Q ( α ) : Q ] = 2 } , {\displaystyle {\mathcal {E}}(j)=\left\{\alpha \in {\mathcal {H}}\...

there is a natural representation of real elliptic curves with shape invariant j ≥ 1 as ellipses in the hyperbolic plane H 2 {\displaystyle \mathbb {H}...

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