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: Kummer pairing | Statement: [Kummer theory, relatesTo, Kummer pairing]

Target entity: Kummer pairing
Context triple: [Kummer theory, relatesTo, Kummer pairing]

• A. Weil pairing
  The Weil pairing is a bilinear, alternating, non-degenerate pairing on the torsion points of an elliptic curve, fundamental in number theory and modern cryptography.
• B. Tate pairing
  The Tate pairing is a bilinear, non-degenerate pairing on the points of an elliptic curve (or abelian variety) over a finite field, fundamental in number theory and widely used in pairing-based cryptography.
• C. Cassels–Tate pairing
  The Cassels–Tate pairing is a bilinear pairing on the Tate–Shafarevich group of an abelian variety over a number field that plays a central role in arithmetic geometry and the study of rational points.
• 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. Kronecker pairing
  The Kronecker pairing is a fundamental bilinear map in algebraic topology that evaluates cohomology classes on homology classes, linking the two via an integer (or field) value.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Kummer pairing
Target entity description: Kummer pairing is a bilinear map in algebraic number theory that connects units or elements of a field with Galois cohomology, playing a central role in understanding abelian extensions via Kummer theory.

• A. Weil pairing
  The Weil pairing is a bilinear, alternating, non-degenerate pairing on the torsion points of an elliptic curve, fundamental in number theory and modern cryptography.
• B. Tate pairing
  The Tate pairing is a bilinear, non-degenerate pairing on the points of an elliptic curve (or abelian variety) over a finite field, fundamental in number theory and widely used in pairing-based cryptography.
• C. Cassels–Tate pairing
  The Cassels–Tate pairing is a bilinear pairing on the Tate–Shafarevich group of an abelian variety over a number field that plays a central role in arithmetic geometry and the study of rational points.
• 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. Kronecker pairing
  The Kronecker pairing is a fundamental bilinear map in algebraic topology that evaluates cohomology classes on homology classes, linking the two via an integer (or field) value.
• F. None of above. chosen