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Search references for CLASS NUMBER. Phrases containing CLASS NUMBER
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Topics referred to by the same term
mathematics, class number may refer to Class number (group theory), in group theory, is the number of conjugacy classes of a group Class number (number theory)
Class_number
Listing all imaginary quadratic fields with a given class number
In mathematics, the Gauss class number problem (for imaginary quadratic fields), as usually understood, is to provide for each n ≥ 1 {\displaystyle n\geq
Class_number_problem
Formula in number theory
In number theory, the class number formula relates many important invariants of an algebraic number field to a special value of its Dedekind zeta function
Class_number_formula
number fields with class number 1. It is believed that there are infinitely many such number fields, but this has not been proven. The class number of
List of number fields with class number one
List_of_number_fields_with_class_number_one
In number theory, measure of non-unique factorization
In mathematics, the ideal class group (or class group) of an algebraic number field K {\displaystyle K} is the quotient group J K / P K {\displaystyle
Ideal_class_group
In mathematics, the Hurwitz class number H(N), introduced by Adolf Hurwitz, is a modification of the class number of positive definite binary quadratic
Hurwitz_class_number
Japanese planned class of battleships
The Number 13-class battleship was a planned class of four fast battleships to be built for the Imperial Japanese Navy (IJN) during the 1920s. The ships
Number_13-class_battleship
In group theory, equivalence class under the relation of conjugation
conjugacy class of a . {\displaystyle a.} The class number of G {\displaystyle G} is the number of distinct (nonequivalent) conjugacy classes. Conjugacy
Conjugacy_class
Linguistic category of nouns
In linguistics, a noun class is a particular category of nouns. A noun may belong to a given class because of the characteristic features of its referent
Noun_class
Generalization of "n-th" to infinite cases
(α + 1)-th number class is the cardinality immediately following that of the α-th number class. For a limit ordinal α, the α-th number class is the union
Ordinal_number
Natural number
a quadratic field of class number two, where 163 is the largest such (Heegner) number of class one. The twenty-first prime number 73 is the largest member
21_(number)
Natural number
{\displaystyle \mathbb {Q} ({\sqrt {-n}})} has class number 3. There are 307 one-sided noniamonds meaning that it is the number of ways to organize 9 triangles with
300_(number)
Library classification system
numbers for main classes, with fractional decimals allowing expansion for further detail. A library assigns a classification number that unambiguously
Dewey_Decimal_Classification
Natural number
the number of pairs of 23 items and 22nd triangular number, 253. 23 is the smallest discriminant of imaginary quadratic fields with class number 3 (negated)
23_(number)
Finite extension of the rationals
K {\displaystyle K} has class number 1. Given a number field, the class number is often difficult to compute. The class number problem, going back to Gauss
Algebraic_number_field
Quadratic homogeneous polynomial in two variables
in quadratic fields. This allows the class number of a quadratic field to be calculated by counting the number of reduced binary quadratic forms of a
Binary_quadratic_form
Set of topological invariants
particular in algebraic topology and differential geometry, the Stiefel–Whitney classes are a set of topological invariants of a real vector bundle that describe
Stiefel–Whitney_class
Natural number
cyclotomic field Q ( ζ n ) {\displaystyle \mathrm {Q} (\zeta _{n})} has class number 1 {\displaystyle 1} (or unique factorization), preceding 60 (that is
84_(number)
Natural number
which the real quadratic field Q[√p] has class number greater than 1 (namely 3). 79 is the smallest number that cannot be represented as a sum of fewer
79_(number)
Registry number for locomotives and multiple units
Digits 5–8 are a four-digit class number, 9–11 the three-digit serial number of the vehicle within its class. For class numbers for vehicles in the existing
UIC identification marking for tractive stock
UIC_identification_marking_for_tractive_stock
Branch of number theory
group in algebraic geometry). The number of elements in the class group is called the class number of K. The class number of Q(√-5) is 2. This means that
Algebraic_number_theory
Natural number
fifth discriminant of imaginary quadratic fields with class number 5, where the 131st prime number 739 is the fifteenth such discriminant. Meanwhile, there
131_(number)
Concept in algebraic number theory
quadratic field Q ( − d ) {\displaystyle \mathbb {Q} ({\sqrt {-d}})} has class number 1. Equivalently, the ring of algebraic integers of Q ( − d ) {\displaystyle
Heegner_number
French general purpose stealth frigates
The La Fayette class (also known as FL-3000 for "Frégate Légère de 3,000 tonnes", or FLF for Frégate Légère Furtive) is a class of general purpose frigates
La_Fayette-class_frigate
Social class
social class system composed of working class and middle class (with the exception of a small number of wealthy billionaires). The American upper class is
Upper_class
Family of diesel and electric multiple units from Siemens
received the class number 460 by the Eisenbahnbundesamt, the federal railway authority (the unpowered middle carriages have the class number 860). The 15
Siemens_Desiro
Characteristic class for real vector bundles
the Pontryagin classes, named after Lev Pontryagin, are certain characteristic classes of real vector bundles. The Pontryagin classes lie in cohomology
Pontryagin_class
Used to count, measure, and label
natural numbers can be represented by classes of equivalent sets. For instance, the number 3 can be represented as the class of all sets that have exactly three
Number
Natural number
of imaginary quadratic fields with class number of 7, negated (see also Heegner numbers). 71 is the largest number which occurs as a prime factor of an
71_(number)
Natural number
the imaginary quadratic field Q(√–d) has class number = 11. Wikimedia Commons has media related to 167 (number). Prime curiosities: 167 Sloane, N. J. A
167_(number)
Characteristic classes of vector bundles
differential geometry and algebraic geometry, the Chern classes are characteristic classes associated with complex vector bundles. They have since become
Chern_class
Class of American 2-8-0 locomotive built for service overseas during World War II
FS Class 736 class.[citation needed] Algeria, Class 140-U – number unknown Morocco, Class 140-B – number unknown Tunisia, Class 140-250 – number unknown
USATC_S160_Class
Class of 0-6-0 freight engines designed by Oliver Bulleid
produce a highly functional design. The class lasted in service until July 1966, and the first member of the class, number C1, has been preserved by the National
SR_Q1_class
Association of cohomology classes to principal bundles
of characteristic classes of total degree n with the fundamental class. The number of distinct characteristic numbers is the number of monomials of degree
Characteristic_class
The Number 64 class (Chinese: 六十四號; pinyin: Liùshísì Hào), also known as the Monfalcone light cruisers or Monfalcone type light cruisers, was a planned
Number_64-class_cruiser
Hitachi tri-mode train
Stubbings, David (17 March 2026). "Grand Central tweaks Cleethorpes plan - confirms class number of tri-mode sets". Rail Magazine. Retrieved 18 March 2026.
British_Rail_Class_820
Field in algebraic number theory
In algebraic number theory, the Hilbert class field E {\displaystyle E} of a number field K {\displaystyle K} is the maximal abelian unramified extension
Hilbert_class_field
Function whose domain is the positive integers
function "expresses some arithmetical property of n". There is a larger class of number-theoretic functions that do not fit this definition, for example, the
Arithmetic_function
Class of US nuclear ballistic missile submarines
The Ohio class of nuclear-powered submarines includes the United States Navy's 14 ballistic missile submarines (SSBNs) and its 4 cruise missile submarines
Ohio-class_submarine
The EAR 56 class was a class of 1,000 mm (3 ft 3+3⁄8 in) gauge 4-8-2+2-8-4 Garratt-type articulated steam locomotives built by Beyer, Peacock & Co. in
EAR_56_class
Field (mathematics) generated by the square root of an integer
of binary quadratic forms. There remain some unsolved problems. The class number problem is particularly important. For a nonzero square free integer
Quadratic_field
number (or prime) is a natural number greater than 1 that has no divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of
List_of_prime_numbers
Natural number
happy number. 239 is the smallest positive integer d such that the imaginary quadratic field Q(√−d) has class number = 15. 239 is the smallest number that
239_(number)
Family of high-speed electric multiple unit trains
debuted on a class 408 train with line number 17. All subsequent units will be tout the redesigned seating. Like the Velaro D Class 407, the class 408 does
Siemens_Velaro
Class of an Irish rail trainset
number 22531–540,641,741,642,742,643,743,644,744,645,745. There have been attempts to improve the fuel economy of the 22000 Class. In 2008 the class were
IÉ_22000_Class
Class of 3164 German 2-10-0 locomotives
class number now had to consist of 3 figures, the designations 051, 052 and 053 had to be introduced in addition to 050. As a result, the old Class 50
DRB_Class_50
Subfield of number theory
the analytic class number formula, and he factor 1 4 {\displaystyle {\tfrac {1}{4}}} appears because the Gaussian field has class number 1 and contains
Special_values_of_L-functions
Class of prototype electric multiple unit
was renumbered as a Class 316 unit, number 316999. To enable it to work on the AC electrification, a pantograph trailer from a Class 313 unit 313034 was
British Rail Classes 316 and 457
British_Rail_Classes_316_and_457
remainder theorem class field The class field theory concerns abelian extensions of number fields. class number 1. The class number of a number field is the
Glossary_of_number_theory
Class of heavy cruisers built for the Royal Navy of the United Kingdom
The County class was a class of heavy cruisers built for the Royal Navy and Royal Australian Navy in the years between the First and Second World Wars
County-class_cruiser
Part of the Kodaira classification
surfaces of class VII are non-algebraic complex surfaces studied by (Kodaira 1964, 1968) that have Kodaira dimension −∞ and first Betti number 1. Minimal
Surface_of_class_VII
Diesel-electric locomotives used by Philippine National Railways
The 5000 class or the GE U6B units feature number signs when they arrived in 1992, which are also found on the last batch of the 900 Class which consists
PNR_5000_class
Czech diesel motor coach class
repairs and additions that retain the class number, or large refurbishments such as ČD Class 814 or ZSSK Class 813, and have a second modernization since
ČSD_Class_M_152.0
Numbering and classification system
many sub-classes were redesignated to better align the locomotives to be numbered in that sub-class with the sub-class number. Thus, class 47 was originally
British Rail locomotive and multiple unit numbering and classification
British_Rail_locomotive_and_multiple_unit_numbering_and_classification
Grammatical number
linguistics, singulative number and collective number (abbreviated sgv and col) are terms used when the grammatical number for multiple items is the
Singulative_number
Electric tram family built in Melbourne, Australia
Australia. As well as Melbourne, W-class trams operate on tourist and heritage systems across the world. A number of older variants have been withdrawn
W-class_Melbourne_tram
Pattern-recognition performance metrics
a class is the number of true positives (i.e. the number of items correctly labelled as belonging to the positive class) divided by the total number of
Precision_and_recall
Class of Soviet diesel-electric patrol submarines
The Foxtrot class was the NATO reporting name of a class of diesel-electric patrol submarines that were built in the Soviet Union. The Soviet designation
Foxtrot-class_submarine
Class of steam locomotives
Harry Wainwright to become B1 class. Twenty B Class engines were built by Neilson, Reid and Company and numbered 440-459. A further nine were built at the
SER_B_class
E Class Together with the letter representing the number of driving axles, a two-digit numeral following the letter indicates a class. The number distinguishes
Japan Railways locomotive numbering and classification
Japan_Railways_locomotive_numbering_and_classification
British steam locomotives
development of Churchward's 4500 Class with larger side tanks and increased water capacity. 100 were built numbered 4575–4599 and 5500–5574. 15 (Nos.
GWR_4575_Class
Railway locomotive
starting with the 141 class. From the early 1970s onwards several locomotives of this class dropped the "B" prefix from their fleet number when re-liveried
CIÉ_121_Class
Number equal to the sum of its proper divisors
In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number
Perfect_number
Freedom-class cruise ship, launched 2007
Independence of the Seas is a Freedom-class cruise ship operated by Royal Caribbean International. The 15-deck ship was built in the Aker Finnyards Turku
Independence_of_the_Seas
Numerical label used to identify a network interface in an IP network
Each class used successively additional octets in the network identifier, thus reducing the possible number of hosts in the higher-order classes (B and
IP_address
Algebraic integer which represents an ideal in a ring of integers
the Hilbert class field. This means that there is an element of the ring of integers of the Hilbert class field, which is an ideal number, such that the
Ideal_number
South African electric locomotive
receive this class number. The locomotive body is a welded monocoque design, constructed of steel plates and profiled members. The Class 22E locomotive
South_African_Class_22E
Class of 285 Japanese 2-8-2 locomotives
The name consists of a "D" for the four sets of driving wheels and the class number 52 for tender locomotives that the numbers 50 through 99 were assigned
JNR_Class_D52
Study of numbers that are not solutions of polynomials with rational coefficients
and indeed it fails to detect that the number e is transcendental. But his work did provide a larger class of transcendental numbers, now known as Liouville
Transcendental_number_theory
class 600 engines were superheated, fitted with Caprotti valve gear and reclassified as class 625 machines between 1929 and 1933. Their class number changed
FS_Class_625
Overview of locomotive classification in Germany
numbers. For the few classes with existing ordering numbers of four digits, such as class 50 (new base class number 050), the class number was extended into
German locomotive classification
German_locomotive_classification
Designation for departmental locomotives
engineering duties. They were therefore of several different classes, lumped together for numbering purposes. Some locomotives were converted from redundant
British_Rail_Class_97
Group-like structure appearing in global fields
class number of a pure cubic field. Math. Comp. 41 (1983), no. 163, 235–286. MR 0701638 G. W. Dueck, H. C. Williams: Computation of the class number and
Infrastructure (number theory)
Infrastructure_(number_theory)
Classification of power amplifier
In electronics, power amplifier classes are letter symbols applied to different power amplifier types. The class gives a broad indication of an amplifier's
Power_amplifier_classes
Class of German shunting locomotives
the 5 Köf 11 prototypes) were given the class number 332, the 3 slower Köf 10 prototypes received class number 331; when the maximum speed was raised to
DB_Class_Köf_III
international competitive sailing and satisfy a number of criteria regarding the number of boats of that class, their international distribution, and the rules
Recognized_class
international competitive sailing" and satisfy a number of criteria regarding the number of boats of that class, their international distribution, and the rules
International_class
Diesel-electric locomotives used by Philippine National Railways
4 digits, the numbering scheme for the new 900 class has three and seems to follow the numbering scheme of the Manila Railroad 800 class USA locomotives
PNR_900_class
Class of 55 two-cylinder 4-6-2 locomotives
The BR Standard Class 7, otherwise known as the Britannia Class, is a class of 4-6-2 "Pacific" type steam locomotive designed under Robert Riddles for
BR_Standard_Class_7
Class of 69 204hp diesel-mechanical shunting locomotives
The British Rail Class D2/5 built by Andrew Barclay Sons & Co. were reported in several sources as having received the TOPS class number 05, though this
British_Rail_Class_05
Class of Polish electric locomotives
painted in the livery in February 2008. Szóstka ("The six") – from the class number Anglik ("Englishman") – from the country of origin Polish locomotives
PKP_class_EU06
the ideal class group. The ray class group is finite. Its order is the ray class number. The ray class number is divisible by the class number of K. Lang
Modulus (algebraic number theory)
Modulus_(algebraic_number_theory)
Number
0 (zero, /ˈziː.roʊ/) is a number representing an empty quantity. Adding (or subtracting) 0 to any number leaves that number unchanged; in mathematical
0
Class of Indonesian diesel-hydraulic locomotives
(33 m/s). The earlier BB301 class number 01–45 was powered by a Maybach Mercedes-Benz 836B diesel engine, while the latter number 51–55 was powered by MTU
Indonesian Railways Class BB301
Indonesian_Railways_Class_BB301
Proposed American battleship class
The Trump-class battleship is a proposed nuclear-powered guided-missile warship for the United States Navy, announced by U.S. president Donald Trump in
Trump-class_battleship
Class of 4-4-0 passenger tank locomotive
LSWR numbering policy, the number of the first locomotive of a new design became the number of the class. Since the first locomotive was numbered 46, the
LSWR_46_class
Biquadratic field Quadratic reciprocity Ideal class group Dirichlet's unit theorem Discriminant of an algebraic number field Ramification (mathematics) Root of
List of algebraic number theory topics
List_of_algebraic_number_theory_topics
B class steam locomotive
team found a stamp marking "B 4977". … 19B's works number was 3518 whilst 4977 is an identical B class but was built 14 years later in 1903. Holden, Michael
DHR_B_Class_778
Mian–Chowla sequence 1525 = heptagonal number, 1526 = number of conjugacy classes in the alternating group A27 1527 = number of 2-dimensional partitions of 11
1000_(number)
Class of British electric multiple unit trains (1979-2019)
network, covering for the withdrawal and scrapping of the Class 303 fleet. A small number of Class 314 units also worked Inverclyde Line services to Gourock
British_Rail_Class_314
The EAR 29 class was a class of oil-burning 1,000 mm (3 ft 3+3⁄8 in) gauge 2-8-2 steam locomotives based upon the Nigerian Railways River class. Thirty-one
EAR_29_class
Numbering used by New South Wales Government Railways
road number. A letter was selected arbitrarily and placed before the first number allotted to each class. e.g. the 93-class became the A.93-class. Letters
NSWGR steam locomotive classification
NSWGR_steam_locomotive_classification
West Germanic language
copula verb to be. The seven word classes are exemplified in this sample sentence: English nouns are only inflected for number and possession. New nouns can
English_language
Steam locomotive built in Glasgow in 1891
North British Railway C Class number 673 Maude is North British Railway C class 0-6-0 tender engine, that was built by Neilson & Co at the Hyde Park Works
NBR_C_Class_673_Maude
Natural number
mathematical proof that 47 was equal to all other integers. The number became a meme among the class, which spread once the academic year began and snowballed
47_(number)
Class of 0-6-0 pannier tank steam locomotives
The GWR 5700 Class (or 57xx class) is a class of 0-6-0PT steam locomotive built by the Great Western Railway (GWR) and British Railways (BR) between 1929
GWR_5700_Class
Airline concept
A business class airline is an airline concept which emerged during the mid-first decade of the 21st century a number of airlines that operated all-business
Business_class_airline
based on that fitted to the 1905 rebuild of his first double-single, T7 class number 720 of 1897; and had a long firebox with a sloping grate. This resulted
LSWR_D15_class
Diesel-electric locomotives used by Philippine National Railways
2500 class is a class of 43 GE U10B Diesel Electric Locomotives first introduced in 1965 with the delivery of the first 13 locomotives of the class. The
PNR_2500_class
identified by a seven-digit vehicle number that consists of a three-digit class number, a three-digit serial number, and a check digit, the latter separated
DB_locomotive_classification
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CLASS NUMBER