mathematics, the conductor of an elliptic curve over the field of rational numbers (or more generally a local or global field) is an integral ideal, which...

mathematics, the rank of an elliptic curve is the rational Mordell–Weil rank of an elliptic curve E {\displaystyle E} defined over the field of rational numbers...

In number theory, the modularity theorem states that elliptic curves over the field of rational numbers are related to modular forms in a particular way...

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 defined...

modular elliptic curve is an elliptic curve E that admits a parametrization X0(N) → E by a modular curve. This is not the same as a modular curve that happens...

corresponding Frey curve Eap,bp,cp is an elliptic curve whose minimal discriminant Δ is equal to 2−8 (abc)2p and whose conductor N is the radical of abc, i.e....

functional equation of the Artin L-function. The Artin and Swan representations are used to define the conductor of an elliptic curve or abelian variety...

for the first correct proof. An elliptic curve is a specific type of variety. Let E be an elliptic curve over Q of conductor N. Then, E has good reduction...

Ogg's formula is either of two things named after Andrew Ogg: Ogg's formula for the conductor of an elliptic curve The Grothendieck–Ogg–Shafarevich formula...

By a theorem of Henri Carayol, if an elliptic curve E is modular then its conductor, an isogeny invariant described originally in terms of cohomology,...

In the theory of elliptic curves, Tate's algorithm takes as input an integral model of an elliptic curve E over Q {\displaystyle \mathbb {Q} } , or more...

of rational solutions to equations defining an elliptic curve. It is an open problem in the field of number theory and is widely recognized as one of...

part of the 1960s. It applies to an elliptic curve E, and the problem it attempts to solve is the prediction of the rank of the elliptic curve over the...

mathematics, the Mestre bound is a bound on the analytic rank of an elliptic curve in terms of its conductor, introduced by Mestre (1986). Brumer bound Mestre, Jean-François...

formula, Ogg's formula for the conductor of an elliptic curve, the Néron–Ogg–Shafarevich criterion and the 1975 characterization of supersingular primes, the...

number theory, Szpiro's conjecture relates to the conductor and the discriminant of an elliptic curve. In a slightly modified form, it is equivalent to...

etale cohomology of a regular model of a variety over a local field and proves it for a curve. The deepest result about the Bloch conductor is its equality...

way for polynomials or for elements of a commutative ring. Eisenstein Eisenstein series elliptic curve Elliptic curve Erdős Erdős–Kac theorem Euclid's lemma...

those other curves, such as elliptic coordinates. The system is based on two foci F1 and F2. Referring to the figure at right, the σ-coordinate of a point...

is one in a suite of programs for computing elliptic curves over rational numbers. Other programs in the suite compute conductors, torsion subgroups...

Microstrip is a type of electrical transmission line which can be fabricated with any technology where a conductor is separated from a ground plane by...

characteristic of a complete curve with coefficients in an abelian variety or constructible sheaf, in terms of local data involving the Swan conductor. Andrew...

characters occur in class field theory and the theory of complex multiplication. Indeed let E be an elliptic curve defined over a number field F with complex multiplication...

Math. 1923 Hasse diagram Hasse invariant of an algebra Hasse invariant of an elliptic curve Hasse invariant of a quadratic form Artin–Hasse exponential...

(n)}{n}}={\frac {\varpi }{4}}} where L {\displaystyle L} is the L-function of the elliptic curve E : y 2 = x 3 − x {\displaystyle E:\,y^{2}=x^{3}-x} over Q {\displaystyle...

propulsion system. Calculation of the magnetic field at points off the center line requires more complex mathematics involving elliptic integrals that require...

^{2n}} or an elliptic curve E {\displaystyle E} over a finite field F q {\displaystyle \mathbb {F} _{q}} . 2.  An abelian scheme is a (flat) family of abelian...

discriminant of an elliptic curve with its conductor. His conjecture inspired the abc conjecture, which was later shown to be equivalent to a modified form of Szpiro's...

separate flat sheets of glass separated with a central vertical metal divide. As curved screen glass became available in the UK at an acceptable price, the...

two conductors depends only on the geometry; the opposing surface area of the conductors and the distance between them; and the permittivity of any dielectric...