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: Hilbert symbol | Statement: [Jacobi symbol, relatedConcept, Hilbert symbol]

Target entity: Hilbert symbol
Context triple: [Jacobi symbol, relatedConcept, Hilbert symbol]

• A. Hasse invariant
  The Hasse invariant is an arithmetic invariant in number theory and algebraic geometry that classifies structures such as quadratic forms or elliptic curves over local and global fields, playing a key role in local-global principles.
• B. Hasse norm theorem
  The Hasse norm theorem is a fundamental result in algebraic number theory that characterizes when an element of a global field is a norm from a cyclic extension by relating this property to its behavior in all completions of the field.
• C. Legendre symbol
  The Legendre symbol is a number-theoretic function that indicates whether an integer is a quadratic residue modulo an odd prime, taking values 1, −1, or 0 accordingly.
• D. 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.
• E. Jacobi symbol
  The Jacobi symbol is a number-theoretic function that generalizes the Legendre symbol and plays a key role in quadratic residues and primality testing in modular arithmetic.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Entity: Hilbert symbol
Triple: [Jacobi symbol, relatedConcept, Hilbert symbol]

The Hilbert symbol is a local arithmetic invariant in number theory that encodes whether a quadratic form represents zero over a given local field, playing a central role in local class field theory and reciprocity laws.

Target entity: Hilbert symbol
Target entity description: The Hilbert symbol is a local arithmetic invariant in number theory that encodes whether a quadratic form represents zero over a given local field, playing a central role in local class field theory and reciprocity laws.

• A. Hasse invariant
  The Hasse invariant is an arithmetic invariant in number theory and algebraic geometry that classifies structures such as quadratic forms or elliptic curves over local and global fields, playing a key role in local-global principles.
• B. Hasse norm theorem
  The Hasse norm theorem is a fundamental result in algebraic number theory that characterizes when an element of a global field is a norm from a cyclic extension by relating this property to its behavior in all completions of the field.
• C. Legendre symbol
  The Legendre symbol is a number-theoretic function that indicates whether an integer is a quadratic residue modulo an odd prime, taking values 1, −1, or 0 accordingly.
• D. 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.
• E. Jacobi symbol
  The Jacobi symbol is a number-theoretic function that generalizes the Legendre symbol and plays a key role in quadratic residues and primality testing in modular arithmetic.
• F. None of above. chosen