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 class polynomial | Statement: [Hilbert class field, relatedTo, Hilbert class polynomial]

Target entity: Hilbert class polynomial
Context triple: [Hilbert class field, relatedTo, Hilbert class polynomial]

• A. Gross–Koblitz formula
  The Gross–Koblitz formula is a result in number theory that expresses Gauss sums in terms of the p-adic gamma function, linking exponential sums over finite fields with p-adic analysis.
• B. Hilbert’s twelfth problem
  Hilbert’s twelfth problem is one of David Hilbert’s famous list of 23 problems, asking for a general explicit class field theory that would generate all abelian extensions of a given number field using special values of analytic functions.
• 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. Richelot isogeny
  The Richelot isogeny is a classical construction in algebraic geometry that gives a specific type of isogeny between principally polarized abelian surfaces, often described via genus-2 curves and their Jacobians.
• E. Hasse bound for elliptic curves
  The Hasse bound for elliptic curves is a fundamental result in number theory that gives tight limits on how far the number of points on an elliptic curve over a finite field can deviate from the size of the field plus one.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Hilbert class polynomial
Target entity description: The Hilbert class polynomial is a key object in algebraic number theory whose roots generate the Hilbert class field of an imaginary quadratic field and play a central role in complex multiplication and explicit class field theory.

• A. Gross–Koblitz formula
  The Gross–Koblitz formula is a result in number theory that expresses Gauss sums in terms of the p-adic gamma function, linking exponential sums over finite fields with p-adic analysis.
• B. Hilbert’s twelfth problem
  Hilbert’s twelfth problem is one of David Hilbert’s famous list of 23 problems, asking for a general explicit class field theory that would generate all abelian extensions of a given number field using special values of analytic functions.
• 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. Richelot isogeny
  The Richelot isogeny is a classical construction in algebraic geometry that gives a specific type of isogeny between principally polarized abelian surfaces, often described via genus-2 curves and their Jacobians.
• E. Hasse bound for elliptic curves
  The Hasse bound for elliptic curves is a fundamental result in number theory that gives tight limits on how far the number of points on an elliptic curve over a finite field can deviate from the size of the field plus one.
• F. None of above. chosen