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: modularity theorem | Statement: [Hecke theory, relatedTo, modularity theorem]

Target entity: modularity theorem
Context triple: [Hecke theory, relatedTo, modularity theorem]

• A. Ribet's theorem
  Ribet's theorem is a result in number theory that linked certain modular forms to Galois representations and played a crucial role in the proof of Fermat's Last Theorem.
• B. modularity conjecture
  The modularity conjecture is a central statement in number theory asserting that every elliptic curve over the rational numbers corresponds to a modular form, a result whose proof underpins the modern proof of Fermat’s Last Theorem.
• C. Eichler–Shimura theory
  Eichler–Shimura theory is a foundational framework in number theory and arithmetic geometry that connects modular forms with the cohomology of modular curves and the theory of elliptic curves.
• D. Taniyama–Shimura–Weil conjecture chosen
  The Taniyama–Shimura–Weil conjecture, now the modularity theorem, asserts that every elliptic curve over the rational numbers is modular and played a central role in the proof of Fermat’s Last Theorem.
• E. Modular curves and the Eisenstein ideal
  "Modular curves and the Eisenstein ideal" is a landmark 1977 paper by Barry Mazur that uses the arithmetic of modular curves and the structure of the Eisenstein ideal in Hecke algebras to prove deep results about rational torsion points on elliptic curves over the rational numbers.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.