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