Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: idele class group | Statement: [Artin reciprocity law, usesConcept, idele class group]

Target entity: idele class group
Context triple: [Artin reciprocity law, usesConcept, idele class group]

• A. idèle class group chosen
  The idèle class group is a fundamental arithmetic object in number theory that encodes global information about a number field via its idèles and plays a central role in class field theory.
• B. Dedekind ideal
  A Dedekind ideal is a type of ideal in ring theory central to algebraic number theory, particularly in the study of Dedekind domains and unique factorization of ideals.
• C. Hilbert class field
  The Hilbert class field of a number field is its maximal unramified abelian extension, central in class field theory as it corresponds to the field’s ideal class group.
• D. Eisenstein ideal
  The Eisenstein ideal is a specific ideal in the Hecke algebra of modular forms that plays a central role in the study of congruences between modular forms and the arithmetic of elliptic curves.
• E. Brauer group
  The Brauer group is an algebraic structure that classifies equivalence classes of central simple algebras over a field (or more general schemes), playing a key role in number theory, algebraic geometry, and cohomology.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.