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: [Birch and Swinnerton-Dyer Conjecture, relatedTo, Modularity theorem]

Target entity: Modularity theorem
Context triple: [Birch and Swinnerton-Dyer Conjecture, relatedTo, Modularity theorem]

• A. 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.
• B. Ramanujan–Petersson conjecture
  The Ramanujan–Petersson conjecture is a fundamental statement in number theory and the theory of modular forms that predicts strong bounds on the Fourier coefficients of modular cusp forms, with deep connections to automorphic forms and the Langlands program.
• C. Birch and Swinnerton-Dyer Conjecture
  The Birch and Swinnerton-Dyer Conjecture is a central unsolved problem in number theory that predicts a deep connection between the arithmetic of rational points on an elliptic curve and the behavior of its associated L-function at a specific value.
• D. Fermat's Last Theorem
  Fermat's Last Theorem is a famous statement in number theory asserting that there are no whole-number solutions to the equation xⁿ + yⁿ = zⁿ for integers n greater than 2, a problem that remained unsolved for over three centuries until it was proved by Andrew Wiles in the 1990s.
• E. Faltings' theorem
  Faltings' theorem is a landmark result in arithmetic geometry that proves every algebraic curve of genus greater than one over a number field has only finitely many rational points.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.